From a76b064fe3e3555b5a9f4e39612d60d56db376a0 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 14 Mar 2025 11:39:45 -0400 Subject: [PATCH 01/82] add intro --- demonstrations/tutorial_qdet_embedding.py | 62 +++++++++++++++++++++++ 1 file changed, 62 insertions(+) create mode 100644 demonstrations/tutorial_qdet_embedding.py diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py new file mode 100644 index 0000000000..878c88227a --- /dev/null +++ b/demonstrations/tutorial_qdet_embedding.py @@ -0,0 +1,62 @@ +r"""Quantum Defect Embedding Theory (QDET) +========================================= +Efficient simulation of complex quantum systems remains a significant challenge in chemistry and +physics. These simulations often require computationally intractable methods for a complete +solution. However, many interesting problems in quantum chemistry and condensed matter physics +feature a strongly correlated region, which requires accurate quantum treatment, embedded within a +larger environment that could be properly treated with cheaper approximations. Examples of such +systems include point defects in materials [], active site of catalysts [], surface phenomenon such +as adsorption [] and many more. Embedding theories serve as powerful tools for effectively +addressing such problems. + +The core idea behind embedding methods is to partition the system and treat the strongly correlated +subsystem accurately, using high-level quantum mechanical methods, while approximating the effects +of the surrounding environment in a way that retains computational efficiency. In this demo, we show +how to implement the quantum defect embedding theory (QDET). The method has been successfully +applied to calculate [...]. An important advantage of QDET is its compatibility with quantum +algorithms as we explain in the following sections. The method can be implemented for calculating +a variety of ground state, excited state and dynamic properties of materials. These make QDET a +powerful method for affordable quantum simulation of materials. + +.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png + :align: center + :width: 70% + :target: javascript:void(0) +""" + +###################################################################### +# title +# --------------------- +# PennyLane +# +# sub +# ^^^^^^^^^^^^^^^^^^^ +# The +# +# .. math:: +# +# H = +# +# The terms :math:`c` +# +# Conclusion +# ---------- +# The +# +# References +# ---------- +# +# .. [#ashcroft] +# +# N. W. Ashcroft, D. N. Mermin, +# "Solid State Physics", Chapter 4, New York: Saunders College Publishing, 1976. +# +# .. [#jovanovic] +# +# D. Jovanovic, R. Gajic, K. Hingerl, +# "Refraction and band isotropy in 2D square-like Archimedean photonic crystal lattices", +# Opt. Express 16, 4048, 2008. +# +# About the authors +# ----------------- +# From 72f5c15e00c0e728dd823646539fad59eff8cfa3 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 14 Mar 2025 16:02:41 -0400 Subject: [PATCH 02/82] add body --- demonstrations/tutorial_qdet_embedding.py | 197 ++++++++++++++++++++-- 1 file changed, 182 insertions(+), 15 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 878c88227a..77d93fb57d 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -25,23 +25,196 @@ """ ###################################################################### -# title -# --------------------- -# PennyLane +# Theory +# ------ +# The core idea in QDET is to construct an effective Hamiltonian that describes the impurity +# subsystem and also accounts for the interactions between the impurity subsystem and the +# environment as # -# sub -# ^^^^^^^^^^^^^^^^^^^ -# The +# .. math:: +# +# H^{eff} = \sum_{ij}^{A} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl}^{A} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, +# +# where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and +# two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. +# This Hamiltonian describes a simplified representations of the complex quantum systems that is +# computationally tractable and properly captures the essential physics of the problem. The +# effective integrals :math:`t, v` can be obtained by fitting experimental results or may be +# derived from first-principles calculations []. +# +# A QDET calculation typically starts by obtaining a meanfield approximation of the whole system +# using efficient quantum chemistry methods such as density functional theory. These calculations +# provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are +# used to construct the effective Hamiltonian which is finally solved by using either a high level +# classical method or a quantum algorithm. Let's implement these steps for an example! +# +# Implementation +# -------------- +# We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy +# defect in diamond []. +# +# Mean field calculations +# ^^^^^^^^^^^^^^^^^^^^^^^ +# We use density functional theory To obtain a mean-field description of the whole system. The DFT +# calculations are performed with the QUANTUM ESPRESSO package. This requires downloading +# parameters needed for each atom type in the system from the QUANTUM ESPRESSO +# `database `_. We have carbon and nitrogen in +# our system which can be downloaded with + +wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf +wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf + +############################################################################## +# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` +# contains information about the system and details of the DFT calculations. More details on +# how to construct the input file can be found in QUANTUM ESPRESSO +# `documentation `_ page. +# +# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: +mpirun -n 2 pw.x -i pw.in > pw.out + + +# Identify the impurity +# ^^^^^^^^^^^^^^^^^^^^^ +# Once we have obtained the meanfield description, we can identify our impurity by finding +# the states that are localized in real space. We can identify these localized states using the +# localization factor defined as []: # # .. math:: # -# H = +# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^ # -# The terms :math:`c` +# We will use the WEST program to compute the localization factor. This requires creating another +# input file ``westpp.in`` as shown below. + +westpp_control: + westpp_calculation: L # triggers the calculation of the localization factor + westpp_range: # defines the range of states toe compute the localization factor + - 1 # start from the first state + - 176 # use all the 176 state + westpp_box: # specifies the parameter of the box in atomic units for integration + - 6.19 # + - 10.19 + - 6.28 + - 10.28 + - 6.28 + - 10.28 + +############################################################################## +# We can execute this calculation as + +mpirun -n 2 westpp.x -i westpp.in > westpp.out + +############################################################################## +# This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required +# to run the calculation are large, the WEST output file needed for the next step can be +# directly downloaded as: + +mkdir -p west.westpp.save +wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json + +############################################################################## +# We can now plot the computed localization factor for each of the states: + +import json +import numpy as np +import matplotlib.pyplot as plt + +with open('west.westpp.save/westpp.json','r') as f: + data = json.load(f) + +y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') +x = np.array([i+1 for i in range(y.shape[0])]) + +plt.plot(x,y,'o') +plt.axhline(y=0.08,linestyle='--',color='red') + +plt.xlabel('KS index') +plt.ylabel('Localization factor') + +plt.show() + +############################################################################## +# From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals +# with low and high localization factor. For the purpose of defining an impurity, we need +# highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals +# that have a localization factor > 0.06 for our active space. We'll use these orbitals for +# the calculation of the parameters for the effective Hamiltonian in the following section. +# +# Effective Hamiltonian +# ^^^^^^^^^^^^^^^^^^^^^ +# The next and probably most important steps in QDET is to define the effective one-body and +# two-body integrals for the impurity. The effective two-body integrals, $v^{eff}$ are computed +# first as matrix elements of the partially screened static Coulomb potential $W_0^{R}$. +# $$v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}$$ +# $W_0^R$, results from screening the bare Coulomb potential, $v$, with the reduced polarizability, +# $P_0^R = P - P_{imp}$, where $P$ is the system's polarizability and $P_{imp}$ is the impurity's +# polarizability. However, this definition of the effective interaction, $v_{eff}$, introduces +# double counting of electrostatic and exchange-correlation effects for the impurity: once via +# density functional theory (DFT) and again via the high-level method. +# Therefore, once $v^{eff}$ is obtained, the one-body term $t^{eff}$ is then modified by subtracting +# from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange +# correlation interactions in the active space. +# +# $$t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}$$ +# +# In WEST, these parameters for the effective Hamiltonian are calculated by using the wfreq.x +# executable. The program will: (i) compute the quasiparticle energies, (ii) compute the +# partially screened Coulomb potential, and (iii) finally compute the parameters of the +# effective Hamiltonian. The input file for such a calculation is shown below: + +wstat_control: + wstat_calculation: S + n_pdep_eigen: 512 + trev_pdep: 0.00001 + +wfreq_control: + wfreq_calculation: XWGQH + macropol_calculation: C + l_enable_off_diagonal: true + n_pdep_eigen_to_use: 512 + qp_bands: [87, 122, 123, 126, 127, 128] + n_refreq: 300 + ecut_refreq: 2.0 + +############################################################################## +# We now construct the effective Hamiltonian: + +from westpy.qdet import QDETResult + +mkdir -p west.wfreq.save +wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json + +effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') + +############################################################################## +# The final step is to solve for this effective Hamiltonian using a high level method. We can +# use the WESTpy package as: + +solution = effective_hamiltonian.solve() + +############################################################################## +# We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This +# requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: + +from pennylane.qchem import one_particle, two_particle, observable +import numpy as np + +effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') + +one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri + +t = one_particle(one_e[0]) +v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) +qubit_op = observable([t, v], mapping="jordan_wigner") + +############################################################################## +# The ground state energy of the Hamiltonian is identical to the one obtained before. # # Conclusion # ---------- -# The +# The quantum density embedding theory is a novel framework for simulating strongly correlated +# quantum systems. # # References # ---------- @@ -51,12 +224,6 @@ # N. W. Ashcroft, D. N. Mermin, # "Solid State Physics", Chapter 4, New York: Saunders College Publishing, 1976. # -# .. [#jovanovic] -# -# D. Jovanovic, R. Gajic, K. Hingerl, -# "Refraction and band isotropy in 2D square-like Archimedean photonic crystal lattices", -# Opt. Express 16, 4048, 2008. -# # About the authors # ----------------- # From 5d88aafe87afa5c411ab2da31f135d494e63fef9 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Tue, 18 Mar 2025 17:40:56 -0400 Subject: [PATCH 03/82] Adressed the comments --- demonstrations/tutorial_qdet_embedding.py | 29 +++++++++++++++++++---- 1 file changed, 24 insertions(+), 5 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 77d93fb57d..94ff805ca6 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -5,15 +5,15 @@ solution. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a larger environment that could be properly treated with cheaper approximations. Examples of such -systems include point defects in materials [], active site of catalysts [], surface phenomenon such -as adsorption [] and many more. Embedding theories serve as powerful tools for effectively +systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such +as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively addressing such problems. The core idea behind embedding methods is to partition the system and treat the strongly correlated subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the surrounding environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to calculate [...]. An important advantage of QDET is its compatibility with quantum +applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating a variety of ground state, excited state and dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation of materials. @@ -214,8 +214,14 @@ # Conclusion # ---------- # The quantum density embedding theory is a novel framework for simulating strongly correlated -# quantum systems. -# +# quantum systems and has been successfully used for studying defects in solids. Applicability of +# QDET is not limited to defects, it can be used for other systems where a strongly correlated subsystem +# is embedded in a weakly correlated environment. QDET is able to surpass the problem of correction of double +# counting of interactions within the active space faced by some other embedding theories +# such as DFT+DMFT. Green's function based formulation of QDET ensures exact removal of double counting +# corrections at GW level of theory, thus removing the approximation present in the initial DFT based formulation. +# Another major advantage of QDET is the ease with which it can be used with quantum computers in a hybrid framework. +# # References # ---------- # @@ -224,6 +230,19 @@ # N. W. Ashcroft, D. N. Mermin, # "Solid State Physics", Chapter 4, New York: Saunders College Publishing, 1976. # +# .. [#Galli] +# +# Joel Davidsson, Mykyta Onizhuk, *et al.*, "Discovery of atomic clock-like spin defects in simple oxides from first principles" +# `ArXiv `__. +# +# .. [#SJRLee] +# Sebastian J. R. Lee, Feizhi Ding, *et al.*, "Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding." +# `ArXiv `__. +# +# .. [#Gagliardi] +# Abhishek Mitra, Matthew Hermes, *et al.*, "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface." +# `ChemRxiv `__. +# # About the authors # ----------------- # From 85a3b23a5d08fc18a1021b37a924aa28e37cc171 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Thu, 20 Mar 2025 09:08:52 -0400 Subject: [PATCH 04/82] Added conclusions --- demonstrations/tutorial_qdet_embedding.py | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 94ff805ca6..a898232367 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -215,13 +215,15 @@ # ---------- # The quantum density embedding theory is a novel framework for simulating strongly correlated # quantum systems and has been successfully used for studying defects in solids. Applicability of -# QDET is not limited to defects, it can be used for other systems where a strongly correlated subsystem +# QDET however is not limited to defects, it can be used for other systems where a strongly correlated subsystem # is embedded in a weakly correlated environment. QDET is able to surpass the problem of correction of double # counting of interactions within the active space faced by some other embedding theories # such as DFT+DMFT. Green's function based formulation of QDET ensures exact removal of double counting -# corrections at GW level of theory, thus removing the approximation present in the initial DFT based formulation. -# Another major advantage of QDET is the ease with which it can be used with quantum computers in a hybrid framework. -# +# corrections at GW level of theory, thus removing the approximation present in the initial DFT based formulation. This +# formulation also helps capture the response properties and provides access to excited state properties. +# Another major advantage of QDET is the ease with which it can be used with quantum computers in a hybrid framework. +# Therefore, We can conlcude here that QDET is a powerful embedding approach for simulating complex quantum systems. +# # References # ---------- # From 28b8c19553eb4a7610f09f832e2b70b6d5f47041 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Thu, 20 Mar 2025 15:11:31 -0400 Subject: [PATCH 05/82] Fixed a definition --- demonstrations/tutorial_qdet_embedding.py | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a898232367..ef49daee6b 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -13,7 +13,8 @@ subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the surrounding environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. An important advantage of QDET is its compatibility with quantum +applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. +An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating a variety of ground state, excited state and dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation of materials. @@ -84,6 +85,7 @@ # # L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^ # +# where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. # We will use the WEST program to compute the localization factor. This requires creating another # input file ``westpp.in`` as shown below. From 3a73910b2cbb4d4034b930d648c69e3f56e37b6b Mon Sep 17 00:00:00 2001 From: soranjh Date: Mon, 28 Apr 2025 14:57:14 -0400 Subject: [PATCH 06/82] git status --- demonstrations/tutorial_qdet_embedding.py | 18 ++++++++++-------- 1 file changed, 10 insertions(+), 8 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index ef49daee6b..55b8b828c4 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -217,14 +217,16 @@ # ---------- # The quantum density embedding theory is a novel framework for simulating strongly correlated # quantum systems and has been successfully used for studying defects in solids. Applicability of -# QDET however is not limited to defects, it can be used for other systems where a strongly correlated subsystem -# is embedded in a weakly correlated environment. QDET is able to surpass the problem of correction of double -# counting of interactions within the active space faced by some other embedding theories -# such as DFT+DMFT. Green's function based formulation of QDET ensures exact removal of double counting -# corrections at GW level of theory, thus removing the approximation present in the initial DFT based formulation. This -# formulation also helps capture the response properties and provides access to excited state properties. -# Another major advantage of QDET is the ease with which it can be used with quantum computers in a hybrid framework. -# Therefore, We can conlcude here that QDET is a powerful embedding approach for simulating complex quantum systems. +# QDET however is not limited to defects, it can be used for other systems where a strongly +# correlated subsystem is embedded in a weakly correlated environment. QDET is able to surpass the +# problem of correction of double counting of interactions within the active space faced by some +# other embedding theories such as DFT+DMFT. Green's function based formulation of QDET ensures +# exact removal of double counting corrections at GW level of theory, thus removing the +# approximation present in the initial DFT based formulation. This formulation also helps capture +# the response properties and provides access to excited state properties. Another major advantage +# of QDET is the ease with which it can be used with quantum computers in a hybrid framework. +# Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex +# quantum systems. # # References # ---------- From 90d95a7414e74898c44ef8c2d8da64c440dc2d30 Mon Sep 17 00:00:00 2001 From: soranjh Date: Mon, 28 Apr 2025 15:42:59 -0400 Subject: [PATCH 07/82] add metadata --- .../tutorial_qdet_embedding.metadata.json | 47 +++++++++++++++++++ 1 file changed, 47 insertions(+) create mode 100644 demonstrations/tutorial_qdet_embedding.metadata.json diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json new file mode 100644 index 0000000000..7c71c93116 --- /dev/null +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -0,0 +1,47 @@ +{ + "title": "Quantum Defect Embedding Theory", + "authors": [ + { + "username": "ddhawan" + } + ], + "dateOfPublication": "2025-04-28T00:00:00+00:00", + "dateOfLastModification": "2025-04-28T00:00:00+00:00", + "categories": [ + "Getting Started", + "How-to" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_spin_hamiltonians.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_spin_hamiltonians.png" + } + ], + "seoDescription": "Learn how to build a Quantum Defect Embedding Theory (QDET) Hamiltonian.", + "doi": "", + "references": [ + { + "id": "ashcroft", + "type": "book", + "title": "Solid State Physics", + "authors": "N. W. Ashcroft, D. N. Mermin", + "year": "1976", + "publisher": "New York: Saunders College Publishing", + "url": "https://en.wikipedia.org/wiki/Ashcroft_and_Mermin" + } + ], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_quantum_chemistry", + "weight": 1.0 + } + ] +} From 4d5caea046bfbc8a0e082fa21857a61fec892775 Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 1 May 2025 10:15:42 -0400 Subject: [PATCH 08/82] disable code --- demonstrations/tutorial_qdet_embedding.py | 186 ++++++++++++---------- 1 file changed, 103 insertions(+), 83 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 55b8b828c4..b71afb5844 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -61,10 +61,12 @@ # parameters needed for each atom type in the system from the QUANTUM ESPRESSO # `database `_. We have carbon and nitrogen in # our system which can be downloaded with - -wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf -wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf - +# +# .. code-block:: python +# +# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf +# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf +# ############################################################################## # Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` # contains information about the system and details of the DFT calculations. More details on @@ -72,9 +74,11 @@ # `documentation `_ page. # # We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: -mpirun -n 2 pw.x -i pw.in > pw.out - - +# +# .. code-block:: python +# +# mpirun -n 2 pw.x -i pw.in > pw.out +# # Identify the impurity # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the meanfield description, we can identify our impurity by finding @@ -88,53 +92,61 @@ # where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. # We will use the WEST program to compute the localization factor. This requires creating another # input file ``westpp.in`` as shown below. - -westpp_control: - westpp_calculation: L # triggers the calculation of the localization factor - westpp_range: # defines the range of states toe compute the localization factor - - 1 # start from the first state - - 176 # use all the 176 state - westpp_box: # specifies the parameter of the box in atomic units for integration - - 6.19 # - - 10.19 - - 6.28 - - 10.28 - - 6.28 - - 10.28 +# +# .. code-block:: python +# +# westpp_control: +# westpp_calculation: L # triggers the calculation of the localization factor +# westpp_range: # defines the range of states toe compute the localization factor +# - 1 # start from the first state +# - 176 # use all the 176 state +# westpp_box: # specifies the parameter of the box in atomic units for integration +# - 6.19 # +# - 10.19 +# - 6.28 +# - 10.28 +# - 6.28 +# - 10.28 ############################################################################## # We can execute this calculation as - -mpirun -n 2 westpp.x -i westpp.in > westpp.out - +# +# .. code-block:: python +# +# mpirun -n 2 westpp.x -i westpp.in > westpp.out +# ############################################################################## # This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required # to run the calculation are large, the WEST output file needed for the next step can be # directly downloaded as: - -mkdir -p west.westpp.save -wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json - +# +# .. code-block:: python +# +# mkdir -p west.westpp.save +# wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json +# ############################################################################## # We can now plot the computed localization factor for each of the states: - -import json -import numpy as np -import matplotlib.pyplot as plt - -with open('west.westpp.save/westpp.json','r') as f: - data = json.load(f) - -y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') -x = np.array([i+1 for i in range(y.shape[0])]) - -plt.plot(x,y,'o') -plt.axhline(y=0.08,linestyle='--',color='red') - -plt.xlabel('KS index') -plt.ylabel('Localization factor') - -plt.show() +# +# .. code-block:: python +# +# import json +# import numpy as np +# import matplotlib.pyplot as plt +# +# with open('west.westpp.save/westpp.json','r') as f: +# data = json.load(f) +# +# y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') +# x = np.array([i+1 for i in range(y.shape[0])]) +# +# plt.plot(x,y,'o') +# plt.axhline(y=0.08,linestyle='--',color='red') +# +# plt.xlabel('KS index') +# plt.ylabel('Localization factor') +# +# plt.show() ############################################################################## # From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals @@ -164,52 +176,60 @@ # executable. The program will: (i) compute the quasiparticle energies, (ii) compute the # partially screened Coulomb potential, and (iii) finally compute the parameters of the # effective Hamiltonian. The input file for such a calculation is shown below: - -wstat_control: - wstat_calculation: S - n_pdep_eigen: 512 - trev_pdep: 0.00001 - -wfreq_control: - wfreq_calculation: XWGQH - macropol_calculation: C - l_enable_off_diagonal: true - n_pdep_eigen_to_use: 512 - qp_bands: [87, 122, 123, 126, 127, 128] - n_refreq: 300 - ecut_refreq: 2.0 - +# +# .. code-block:: python +# +# wstat_control: +# wstat_calculation: S +# n_pdep_eigen: 512 +# trev_pdep: 0.00001 +# +# wfreq_control: +# wfreq_calculation: XWGQH +# macropol_calculation: C +# l_enable_off_diagonal: true +# n_pdep_eigen_to_use: 512 +# qp_bands: [87, 122, 123, 126, 127, 128] +# n_refreq: 300 +# ecut_refreq: 2.0 +# ############################################################################## # We now construct the effective Hamiltonian: - -from westpy.qdet import QDETResult - -mkdir -p west.wfreq.save -wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json - -effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') - +# +# .. code-block:: python +# +# from westpy.qdet import QDETResult +# +# mkdir -p west.wfreq.save +# wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json +# +# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') +# ############################################################################## # The final step is to solve for this effective Hamiltonian using a high level method. We can # use the WESTpy package as: - -solution = effective_hamiltonian.solve() - +# +# .. code-block:: python +# +# solution = effective_hamiltonian.solve() +# ############################################################################## # We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This # requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: - -from pennylane.qchem import one_particle, two_particle, observable -import numpy as np - -effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') - -one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri - -t = one_particle(one_e[0]) -v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -qubit_op = observable([t, v], mapping="jordan_wigner") - +# +# .. code-block:: python +# +# from pennylane.qchem import one_particle, two_particle, observable +# import numpy as np +# +# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') +# +# one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri +# +# t = one_particle(one_e[0]) +# v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) +# qubit_op = observable([t, v], mapping="jordan_wigner") +# ############################################################################## # The ground state energy of the Hamiltonian is identical to the one obtained before. # From c7ce50ded45d90d1bfb90a911e1e57903e337f50 Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 1 May 2025 10:33:01 -0400 Subject: [PATCH 09/82] fix format --- demonstrations/tutorial_qdet_embedding.py | 15 ++------------- 1 file changed, 2 insertions(+), 13 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index b71afb5844..6b1ab6a16e 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -24,8 +24,6 @@ :width: 70% :target: javascript:void(0) """ - -###################################################################### # Theory # ------ # The core idea in QDET is to construct an effective Hamiltonian that describes the impurity @@ -67,7 +65,6 @@ # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf # -############################################################################## # Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` # contains information about the system and details of the DFT calculations. More details on # how to construct the input file can be found in QUANTUM ESPRESSO @@ -107,15 +104,13 @@ # - 10.28 # - 6.28 # - 10.28 - -############################################################################## +# # We can execute this calculation as # # .. code-block:: python # # mpirun -n 2 westpp.x -i westpp.in > westpp.out # -############################################################################## # This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required # to run the calculation are large, the WEST output file needed for the next step can be # directly downloaded as: @@ -125,7 +120,6 @@ # mkdir -p west.westpp.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json # -############################################################################## # We can now plot the computed localization factor for each of the states: # # .. code-block:: python @@ -147,8 +141,7 @@ # plt.ylabel('Localization factor') # # plt.show() - -############################################################################## +# # From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals # with low and high localization factor. For the purpose of defining an impurity, we need # highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals @@ -193,7 +186,6 @@ # n_refreq: 300 # ecut_refreq: 2.0 # -############################################################################## # We now construct the effective Hamiltonian: # # .. code-block:: python @@ -205,7 +197,6 @@ # # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') # -############################################################################## # The final step is to solve for this effective Hamiltonian using a high level method. We can # use the WESTpy package as: # @@ -213,7 +204,6 @@ # # solution = effective_hamiltonian.solve() # -############################################################################## # We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This # requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: # @@ -230,7 +220,6 @@ # v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) # qubit_op = observable([t, v], mapping="jordan_wigner") # -############################################################################## # The ground state energy of the Hamiltonian is identical to the one obtained before. # # Conclusion From f08c4ba554fefcbabe90f0e8e5a6cda6accb168b Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 1 May 2025 11:37:27 -0400 Subject: [PATCH 10/82] fix format --- demonstrations/tutorial_qdet_embedding.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 6b1ab6a16e..a800dada53 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -23,7 +23,10 @@ :align: center :width: 70% :target: javascript:void(0) + """ + +############################################# # Theory # ------ # The core idea in QDET is to construct an effective Hamiltonian that describes the impurity From e336aac9f1084e4877adcd12c9443356a15c380b Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 1 May 2025 11:49:46 -0400 Subject: [PATCH 11/82] fix math --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a800dada53..c06cc37af6 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -87,7 +87,7 @@ # # .. math:: # -# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^ +# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 # # where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. # We will use the WEST program to compute the localization factor. This requires creating another From 4dcbdebc74481b3b73e0b9180df3d696150d0912 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:43:44 -0400 Subject: [PATCH 12/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index c06cc37af6..209c02d1ae 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -227,7 +227,7 @@ # # Conclusion # ---------- -# The quantum density embedding theory is a novel framework for simulating strongly correlated +# The quantum defect embedding theory is a novel framework for simulating strongly correlated # quantum systems and has been successfully used for studying defects in solids. Applicability of # QDET however is not limited to defects, it can be used for other systems where a strongly # correlated subsystem is embedded in a weakly correlated environment. QDET is able to surpass the From 1613232dc5652e31a4c63251c594b24d615bcd31 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:44:08 -0400 Subject: [PATCH 13/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 209c02d1ae..0139a3d2b2 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -82,7 +82,7 @@ # Identify the impurity # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the meanfield description, we can identify our impurity by finding -# the states that are localized in real space. We can identify these localized states using the +# the states that are localized in real space around the defect region. We can identify these localized states using the # localization factor defined as []: # # .. math:: From e8c6d1d7bd2e6f993c6e809cae84e573046d225f Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:45:00 -0400 Subject: [PATCH 14/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 0139a3d2b2..41193eff93 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -4,7 +4,7 @@ physics. These simulations often require computationally intractable methods for a complete solution. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a -larger environment that could be properly treated with cheaper approximations. Examples of such +larger environment that could be properly treated with cheaper approximations. For example, systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively addressing such problems. From c5ff1422ba2412fb99ca0e46d28ea86f555e9361 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:45:27 -0400 Subject: [PATCH 15/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 41193eff93..4088e4d5b1 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -5,7 +5,7 @@ solution. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a larger environment that could be properly treated with cheaper approximations. For example, -systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such +this is the case for point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively addressing such problems. From 906bb1a53266ce556047a328ba9cca220a4e66ef Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:51:13 -0400 Subject: [PATCH 16/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 4088e4d5b1..7242d0c29a 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -16,7 +16,7 @@ applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating -a variety of ground state, excited state and dynamic properties of materials. These make QDET a +ground and excited states, as well as dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation of materials. .. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png From 4535791930cbc7de61516e12e4580fdee4dceea3 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:51:41 -0400 Subject: [PATCH 17/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 7242d0c29a..b86eeca106 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -39,7 +39,7 @@ # # where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and # two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. -# This Hamiltonian describes a simplified representations of the complex quantum systems that is +# This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The # effective integrals :math:`t, v` can be obtained by fitting experimental results or may be # derived from first-principles calculations []. From bf9510ee04d4e98e18eb917865128df6bba30575 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:51:57 -0400 Subject: [PATCH 18/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index b86eeca106..04cc1d58f1 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -41,7 +41,7 @@ # two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. # This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The -# effective integrals :math:`t, v` can be obtained by fitting experimental results or may be +# effective integrals :math:`t, v` are obtained # derived from first-principles calculations []. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system From 9ac57d60397e6bb5f09a0ac58da0812f4da3e436 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:52:24 -0400 Subject: [PATCH 19/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 04cc1d58f1..2d6f3e2bce 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -42,7 +42,7 @@ # This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The # effective integrals :math:`t, v` are obtained -# derived from first-principles calculations []. +# from first-principles calculations []. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system # using efficient quantum chemistry methods such as density functional theory. These calculations From f8bf9c191626bc3a5e5e8f70002fd2e98bdaafe5 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 16:52:39 -0400 Subject: [PATCH 20/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 2d6f3e2bce..42fe6a4b23 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -45,7 +45,7 @@ # from first-principles calculations []. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system -# using efficient quantum chemistry methods such as density functional theory. These calculations +# using efficient mean field methods such as density functional theory. These calculations # provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are # used to construct the effective Hamiltonian which is finally solved by using either a high level # classical method or a quantum algorithm. Let's implement these steps for an example! From b42e5c31250a6868e676cff40d3f55d92fa18fc9 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 6 May 2025 17:01:36 -0400 Subject: [PATCH 21/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 42fe6a4b23..90ac7642f5 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -59,7 +59,7 @@ # ^^^^^^^^^^^^^^^^^^^^^^^ # We use density functional theory To obtain a mean-field description of the whole system. The DFT # calculations are performed with the QUANTUM ESPRESSO package. This requires downloading -# parameters needed for each atom type in the system from the QUANTUM ESPRESSO +# the pseudopotentials for each atomic species in the system from the QUANTUM ESPRESSO # `database `_. We have carbon and nitrogen in # our system which can be downloaded with # From 09a667a87ae97c096a49a0f9ddcfec35c7f006f0 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 11:34:24 -0400 Subject: [PATCH 22/82] Addressed comments --- .../tutorial_qdet_embedding.metadata.json | 96 +++++++++++++------ demonstrations/tutorial_qdet_embedding.py | 54 ++++++----- 2 files changed, 99 insertions(+), 51 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index 7c71c93116..f37a002987 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -1,47 +1,87 @@ { "title": "Quantum Defect Embedding Theory", - "authors": [ - { - "username": "ddhawan" - } - ], - "dateOfPublication": "2025-04-28T00:00:00+00:00", - "dateOfLastModification": "2025-04-28T00:00:00+00:00", - "categories": [ - "Getting Started", - "How-to" - ], + "authors": [{"username": "ddhawan"}, {"username": "soran"}], + "dateOfPublication": "2025-05-09T00:00:00+00:00", + "dateOfLastModification": "2025-05-09T00:00:00+00:00", + "categories": ["Quantum Chemistry"], "tags": [], "previewImages": [ { "type": "thumbnail", - "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_spin_hamiltonians.png" + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_spin_hamiltonians.png", }, { "type": "large_thumbnail", - "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_spin_hamiltonians.png" - } + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_spin_hamiltonians.png", + }, ], "seoDescription": "Learn how to build a Quantum Defect Embedding Theory (QDET) Hamiltonian.", "doi": "", "references": [ { - "id": "ashcroft", - "type": "book", - "title": "Solid State Physics", - "authors": "N. W. Ashcroft, D. N. Mermin", - "year": "1976", - "publisher": "New York: Saunders College Publishing", - "url": "https://en.wikipedia.org/wiki/Ashcroft_and_Mermin" - } + "id": "Galli", + "type": "article", + "title": "Discovery of atomic clock-like spin defects in simple oxides from first principles", + "authors": "Davidsson, Joel and Onizhuk, Mykyta and Vorwerk, Christian and Galli, Giulia", + "year": "2024", + "publisher": "", + "journal": "", + "url": "https://arxiv.org/pdf/2302.07523", + }, + { + "id": "SJRLee", + "type": "article", + "title": "Analytical gradients for projection-based wavefunction-in-DFT embedding", + "authors": "Lee, Sebastian JR and Ding, Feizhi and Manby, Frederick R and Miller, Thomas F", + "year": "2019", + "publisher": "", + "journal": "", + "url": "https://arxiv.org/pdf/1903.05830", + }, + { + "id": "Gagliardi", + "type": "article", + "title": "Periodic density matrix embedding for co adsorption on the mgo (001) surface", + "authors": "Mitra, Abhishek and Hermes, Matthew R and Cho, Minsik and Agarawal, Valay and Gagliardi, Laura", + "year": "2022", + "publisher": "", + "journal": "", + "url": "https://chemrxiv.org/engage/chemrxiv/article-details/62b0b0c40bba5d82606d2cae", + }, + { + "id": "Galli2", + "type": "article", + "title": "Green’s function formulation of quantum defect embedding theory", + "authors": "Sheng, Nan and Vorwerk, Christian and Govoni, Marco and Galli, Giulia", + "year": "2022", + "publisher": "", + "journal": "", + "url": "https://arxiv.org/pdf/2203.05493", + }, + { + "id": "Modji", + "type": "article", + "title": "Quantum simulation of battery materials using ionic pseudopotentials", + "authors": "Zini, Modjtaba Shokrian and Delgado, Alain and dos Reis, Roberto and Casares, Pablo Antonio Moreno and Mueller, Jonathan E and Voigt, Arne-Christian and Arrazola, Juan Miguel", + "year": "2023", + "publisher": "", + "journal": "", + "url": "https://arxiv.org/pdf/2302.07981", + }, + { + "id": "Baker", + "type": "article", + "title": "Simulating optically active spin defects with a quantum computer", + "authors": "Baker, Jack S and Casares, Pablo AM and Zini, Modjtaba Shokrian and Thik, Jaydeep and Banerjee, Debasish and Ling, Chen and Delgado, Alain and Arrazola, Juan Miguel", + "year": "2024", + "publisher": "", + "journal": "", + "url": "https://arxiv.org/pdf/2405.13115", + }, ], "basedOnPapers": [], "referencedByPapers": [], "relatedContent": [ - { - "type": "demonstration", - "id": "tutorial_quantum_chemistry", - "weight": 1.0 - } - ] + {"type": "demonstration", "id": "tutorial_quantum_chemistry", "weight": 1.0} + ], } diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 90ac7642f5..2e2ec31fd1 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,19 +1,20 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Efficient simulation of complex quantum systems remains a significant challenge in chemistry and -physics. These simulations often require computationally intractable methods for a complete -solution. However, many interesting problems in quantum chemistry and condensed matter physics +Performing efficient simulations of advances materials and molecules remains a significant +challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of +available methods. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a larger environment that could be properly treated with cheaper approximations. For example, this is the case for point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively -addressing such problems. +addressing such problems by capturing the strong electronic correlations in the active region with high accuracy +while accounting for the environment in a more approximate manner. The core idea behind embedding methods is to partition the system and treat the strongly correlated subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the surrounding environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. +applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating ground and excited states, as well as dynamic properties of materials. These make QDET a @@ -29,7 +30,7 @@ ############################################# # Theory # ------ -# The core idea in QDET is to construct an effective Hamiltonian that describes the impurity +# QDET allows us to construct an effective Hamiltonian that describes the impurity # subsystem and also accounts for the interactions between the impurity subsystem and the # environment as # @@ -42,7 +43,7 @@ # This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The # effective integrals :math:`t, v` are obtained -# from first-principles calculations []. +# from first-principles calculations [#Galli2]. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system # using efficient mean field methods such as density functional theory. These calculations @@ -53,13 +54,14 @@ # Implementation # -------------- # We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy -# defect in diamond []. +# defect in diamond. # # Mean field calculations # ^^^^^^^^^^^^^^^^^^^^^^^ # We use density functional theory To obtain a mean-field description of the whole system. The DFT # calculations are performed with the QUANTUM ESPRESSO package. This requires downloading -# the pseudopotentials for each atomic species in the system from the QUANTUM ESPRESSO +# the pseudopotentials [#Modji] for each atomic species +# in the system from the QUANTUM ESPRESSO # `database `_. We have carbon and nitrogen in # our system which can be downloaded with # @@ -83,14 +85,14 @@ # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the meanfield description, we can identify our impurity by finding # the states that are localized in real space around the defect region. We can identify these localized states using the -# localization factor defined as []: +# localization factor defined as [#Galli2]: # # .. math:: # # L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 # # where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. -# We will use the WEST program to compute the localization factor. This requires creating another +# We will use the `WEST `_ program to compute the localization factor. This requires creating another # input file ``westpp.in`` as shown below. # # .. code-block:: python @@ -159,10 +161,10 @@ # $$v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}$$ # $W_0^R$, results from screening the bare Coulomb potential, $v$, with the reduced polarizability, # $P_0^R = P - P_{imp}$, where $P$ is the system's polarizability and $P_{imp}$ is the impurity's -# polarizability. However, this definition of the effective interaction, $v_{eff}$, introduces -# double counting of electrostatic and exchange-correlation effects for the impurity: once via -# density functional theory (DFT) and again via the high-level method. -# Therefore, once $v^{eff}$ is obtained, the one-body term $t^{eff}$ is then modified by subtracting +# polarizability. Since this leads to the inclusion of electrostatic +# and exchange-correlation effects for the active electrons, we remove these interactions from the +# the Kohn-Sham Hamiltonian, $H^{KS}$, to avoid double counting them. +# Therefore, once $v^{eff}$ is obtained, the one-body term $t^{eff}$ is then obtained by subtracting # from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange # correlation interactions in the active space. # @@ -236,20 +238,14 @@ # exact removal of double counting corrections at GW level of theory, thus removing the # approximation present in the initial DFT based formulation. This formulation also helps capture # the response properties and provides access to excited state properties. Another major advantage -# of QDET is the ease with which it can be used with quantum computers in a hybrid framework. +# of QDET is the ease with which it can be used with quantum computers in a hybrid framework[#Baker]. # Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex # quantum systems. -# +# # References # ---------- # -# .. [#ashcroft] -# -# N. W. Ashcroft, D. N. Mermin, -# "Solid State Physics", Chapter 4, New York: Saunders College Publishing, 1976. -# # .. [#Galli] -# # Joel Davidsson, Mykyta Onizhuk, *et al.*, "Discovery of atomic clock-like spin defects in simple oxides from first principles" # `ArXiv `__. # @@ -261,6 +257,18 @@ # Abhishek Mitra, Matthew Hermes, *et al.*, "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface." # `ChemRxiv `__. # +# .. [#Galli2] +# Nan Sheng, Christian Vorwerk, *et al.*, "Green's function formulation of quantum defect embedding theory" +# `Arxiv `__. +# +# .. [#Modji] +# Modjtaba S. Zini, Alain Delgado, *et al.*, "Quantum simulation of battery materials using ionic pseudopotentials" +# `ArXiv `__. +# +# .. [#Baker] +# Jack S. Baker, Pablo A. M. Casares, *et al.*, "Simulating optically-active spin defects with a quantum computer" +# `ArXiv `__. +# # About the authors # ----------------- # From 35a9252adde86a522207cd86f9185f893105e408 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 11:41:40 -0400 Subject: [PATCH 23/82] Updated references --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 2e2ec31fd1..b4fdf35656 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -14,7 +14,7 @@ subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the surrounding environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. +applied to study defects in CaO[#Galli] and to calculate excitations of the negatively charged NV center in diamond[#Galli2]. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating ground and excited states, as well as dynamic properties of materials. These make QDET a From ad24ae8d2347bce3166a5ee55f48a76f42548a31 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 12:47:29 -0400 Subject: [PATCH 24/82] Fixed rendering issue --- tutorial_qdet_embedding.py | 280 +++++++++++++++++++++++++++++++++++++ 1 file changed, 280 insertions(+) create mode 100644 tutorial_qdet_embedding.py diff --git a/tutorial_qdet_embedding.py b/tutorial_qdet_embedding.py new file mode 100644 index 0000000000..99f987f2c0 --- /dev/null +++ b/tutorial_qdet_embedding.py @@ -0,0 +1,280 @@ +r"""Quantum Defect Embedding Theory (QDET) +========================================= +Performing efficient simulations of advances materials and molecules remains a significant +challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of +available methods. However, many interesting problems in quantum chemistry and condensed matter physics +feature a strongly correlated region, which requires accurate quantum treatment, embedded within a +larger environment that could be properly treated with cheaper approximations. For example, +this is the case for point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such +as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively +addressing such problems by capturing the strong electronic correlations in the active region with high accuracy +while accounting for the environment in a more approximate manner. + +The core idea behind embedding methods is to partition the system and treat the strongly correlated +subsystem accurately, using high-level quantum mechanical methods, while approximating the effects +of the surrounding environment in a way that retains computational efficiency. In this demo, we show +how to implement the quantum defect embedding theory (QDET). The method has been successfully +applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. +An important advantage of QDET is its compatibility with quantum +algorithms as we explain in the following sections. The method can be implemented for calculating +ground and excited states, as well as dynamic properties of materials. These make QDET a +powerful method for affordable quantum simulation of materials. + +.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png + :align: center + :width: 70% + :target: javascript:void(0) + +""" + +############################################# +# Theory +# ------ +# QDET allows us to construct an effective Hamiltonian that describes the impurity +# subsystem and also accounts for the interactions between the impurity subsystem and the +# environment as +# +# .. math:: +# +# H^{eff} = \sum_{ij}^{A} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl}^{A} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, +# +# where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and +# two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. +# This Hamiltonian describes a simplified representation of the complex quantum system that is +# computationally tractable and properly captures the essential physics of the problem. The +# effective integrals :math:`t, v` are obtained +# from first-principles calculations [#Galli2]_. +# +# A QDET calculation typically starts by obtaining a meanfield approximation of the whole system +# using efficient mean field methods such as density functional theory. These calculations +# provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are +# used to construct the effective Hamiltonian which is finally solved by using either a high level +# classical method or a quantum algorithm. Let's implement these steps for an example! +# +# Implementation +# -------------- +# We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy +# defect in diamond. +# +# Mean field calculations +# ^^^^^^^^^^^^^^^^^^^^^^^ +# We use density functional theory To obtain a mean-field description of the whole system. The DFT +# calculations are performed with the QUANTUM ESPRESSO package. This requires downloading +# the pseudopotentials [#Modji]_ for each atomic species +# in the system from the QUANTUM ESPRESSO +# `database `_. We have carbon and nitrogen in +# our system which can be downloaded with +# +# .. code-block:: python +# +# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf +# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf +# +# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` +# contains information about the system and details of the DFT calculations. More details on +# how to construct the input file can be found in QUANTUM ESPRESSO +# `documentation `_ page. +# +# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: +# +# .. code-block:: python +# +# mpirun -n 2 pw.x -i pw.in > pw.out +# +# Identify the impurity +# ^^^^^^^^^^^^^^^^^^^^^ +# Once we have obtained the meanfield description, we can identify our impurity by finding +# the states that are localized in real space around the defect region. We can identify these localized states using the +# localization factor defined as: +# +# .. math:: +# +# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 +# +# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\ohm` [#Galli2]_. +# We will use the `WEST `_ program to compute the localization factor. This requires creating another +# input file ``westpp.in`` as shown below. +# +# .. code-block:: python +# +# westpp_control: +# westpp_calculation: L # triggers the calculation of the localization factor +# westpp_range: # defines the range of states toe compute the localization factor +# - 1 # start from the first state +# - 176 # use all the 176 state +# westpp_box: # specifies the parameter of the box in atomic units for integration +# - 6.19 # +# - 10.19 +# - 6.28 +# - 10.28 +# - 6.28 +# - 10.28 +# +# We can execute this calculation as +# +# .. code-block:: python +# +# mpirun -n 2 westpp.x -i westpp.in > westpp.out +# +# This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required +# to run the calculation are large, the WEST output file needed for the next step can be +# directly downloaded as: +# +# .. code-block:: python +# +# mkdir -p west.westpp.save +# wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json +# +# We can now plot the computed localization factor for each of the states: +# +# .. code-block:: python +# +# import json +# import numpy as np +# import matplotlib.pyplot as plt +# +# with open('west.westpp.save/westpp.json','r') as f: +# data = json.load(f) +# +# y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') +# x = np.array([i+1 for i in range(y.shape[0])]) +# +# plt.plot(x,y,'o') +# plt.axhline(y=0.08,linestyle='--',color='red') +# +# plt.xlabel('KS index') +# plt.ylabel('Localization factor') +# +# plt.show() +# +# From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals +# with low and high localization factor. For the purpose of defining an impurity, we need +# highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals +# that have a localization factor > 0.06 for our active space. We'll use these orbitals for +# the calculation of the parameters for the effective Hamiltonian in the following section. +# +# Effective Hamiltonian +# ^^^^^^^^^^^^^^^^^^^^^ +# The next and probably most important steps in QDET is to define the effective one-body and +# two-body integrals for the impurity. The effective two-body integrals, :math:`v^{eff}` are computed +# first as matrix elements of the partially screened static Coulomb potential :math:`W_0^{R}`. +# +# .. math:: +# +# v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, +# +# :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, +# :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's +# polarizability. Since this leads to the inclusion of electrostatic +# and exchange-correlation effects for the active electrons, we remove these interactions from the +# the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. +# Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting +# from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange +# correlation interactions in the active space. +# +# .. math:: +# +# t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, +# +# In WEST, these parameters for the effective Hamiltonian are calculated by using the wfreq.x +# executable. The program will: (i) compute the quasiparticle energies, (ii) compute the +# partially screened Coulomb potential, and (iii) finally compute the parameters of the +# effective Hamiltonian. The input file for such a calculation is shown below: +# +# .. code-block:: python +# +# wstat_control: +# wstat_calculation: S +# n_pdep_eigen: 512 +# trev_pdep: 0.00001 +# +# wfreq_control: +# wfreq_calculation: XWGQH +# macropol_calculation: C +# l_enable_off_diagonal: true +# n_pdep_eigen_to_use: 512 +# qp_bands: [87, 122, 123, 126, 127, 128] +# n_refreq: 300 +# ecut_refreq: 2.0 +# +# We now construct the effective Hamiltonian: +# +# .. code-block:: python +# +# from westpy.qdet import QDETResult +# +# mkdir -p west.wfreq.save +# wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json +# +# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') +# +# The final step is to solve for this effective Hamiltonian using a high level method. We can +# use the WESTpy package as: +# +# .. code-block:: python +# +# solution = effective_hamiltonian.solve() +# +# We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This +# requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: +# +# .. code-block:: python +# +# from pennylane.qchem import one_particle, two_particle, observable +# import numpy as np +# +# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') +# +# one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri +# +# t = one_particle(one_e[0]) +# v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) +# qubit_op = observable([t, v], mapping="jordan_wigner") +# +# The ground state energy of the Hamiltonian is identical to the one obtained before. +# +# Conclusion +# ---------- +# The quantum defect embedding theory is a novel framework for simulating strongly correlated +# quantum systems and has been successfully used for studying defects in solids. Applicability of +# QDET however is not limited to defects, it can be used for other systems where a strongly +# correlated subsystem is embedded in a weakly correlated environment. QDET is able to surpass the +# problem of correction of double counting of interactions within the active space faced by some +# other embedding theories such as DFT+DMFT. Green's function based formulation of QDET ensures +# exact removal of double counting corrections at GW level of theory, thus removing the +# approximation present in the initial DFT based formulation. This formulation also helps capture +# the response properties and provides access to excited state properties. Another major advantage +# of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. +# Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex +# quantum systems. +# +# References +# ---------- +# +# .. [#Galli] +# Joel Davidsson, Mykyta Onizhuk, *et al.*, "Discovery of atomic clock-like spin defects in simple oxides from first principles" +# `ArXiv `__. +# +# .. [#SJRLee] +# Sebastian J. R. Lee, Feizhi Ding, *et al.*, "Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding." +# `ArXiv `__. +# +# .. [#Gagliardi] +# Abhishek Mitra, Matthew Hermes, *et al.*, "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface." +# `ChemRxiv `__. +# +# .. [#Galli2] +# Nan Sheng, Christian Vorwerk, *et al.*, "Green's function formulation of quantum defect embedding theory" +# `Arxiv `__. +# +# .. [#Modji] +# Modjtaba S. Zini, Alain Delgado, *et al.*, "Quantum simulation of battery materials using ionic pseudopotentials" +# `ArXiv `__. +# +# .. [#Baker] +# Jack S. Baker, Pablo A. M. Casares, *et al.*, "Simulating optically-active spin defects with a quantum computer" +# `ArXiv `__. +# +# About the authors +# ----------------- +# From 62b39fccf93c3c5d76c8a47c804a86b054e59a99 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 12:51:28 -0400 Subject: [PATCH 25/82] Fixed rendering --- .../tutorial_qdet_embedding.metadata.json | 2 +- demonstrations/tutorial_qdet_embedding.py | 34 ++- tutorial_qdet_embedding.py | 280 ------------------ 3 files changed, 21 insertions(+), 295 deletions(-) delete mode 100644 tutorial_qdet_embedding.py diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index f37a002987..be6a4707cb 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -3,7 +3,7 @@ "authors": [{"username": "ddhawan"}, {"username": "soran"}], "dateOfPublication": "2025-05-09T00:00:00+00:00", "dateOfLastModification": "2025-05-09T00:00:00+00:00", - "categories": ["Quantum Chemistry"], + "categories": ["Quantum Chemistry",], "tags": [], "previewImages": [ { diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index b4fdf35656..99f987f2c0 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -14,7 +14,7 @@ subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the surrounding environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to study defects in CaO[#Galli] and to calculate excitations of the negatively charged NV center in diamond[#Galli2]. +applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating ground and excited states, as well as dynamic properties of materials. These make QDET a @@ -43,7 +43,7 @@ # This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The # effective integrals :math:`t, v` are obtained -# from first-principles calculations [#Galli2]. +# from first-principles calculations [#Galli2]_. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system # using efficient mean field methods such as density functional theory. These calculations @@ -60,7 +60,7 @@ # ^^^^^^^^^^^^^^^^^^^^^^^ # We use density functional theory To obtain a mean-field description of the whole system. The DFT # calculations are performed with the QUANTUM ESPRESSO package. This requires downloading -# the pseudopotentials [#Modji] for each atomic species +# the pseudopotentials [#Modji]_ for each atomic species # in the system from the QUANTUM ESPRESSO # `database `_. We have carbon and nitrogen in # our system which can be downloaded with @@ -85,13 +85,13 @@ # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the meanfield description, we can identify our impurity by finding # the states that are localized in real space around the defect region. We can identify these localized states using the -# localization factor defined as [#Galli2]: +# localization factor defined as: # # .. math:: # # L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 # -# where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. +# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\ohm` [#Galli2]_. # We will use the `WEST `_ program to compute the localization factor. This requires creating another # input file ``westpp.in`` as shown below. # @@ -156,19 +156,25 @@ # Effective Hamiltonian # ^^^^^^^^^^^^^^^^^^^^^ # The next and probably most important steps in QDET is to define the effective one-body and -# two-body integrals for the impurity. The effective two-body integrals, $v^{eff}$ are computed -# first as matrix elements of the partially screened static Coulomb potential $W_0^{R}$. -# $$v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}$$ -# $W_0^R$, results from screening the bare Coulomb potential, $v$, with the reduced polarizability, -# $P_0^R = P - P_{imp}$, where $P$ is the system's polarizability and $P_{imp}$ is the impurity's +# two-body integrals for the impurity. The effective two-body integrals, :math:`v^{eff}` are computed +# first as matrix elements of the partially screened static Coulomb potential :math:`W_0^{R}`. +# +# .. math:: +# +# v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, +# +# :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, +# :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's # polarizability. Since this leads to the inclusion of electrostatic # and exchange-correlation effects for the active electrons, we remove these interactions from the -# the Kohn-Sham Hamiltonian, $H^{KS}$, to avoid double counting them. -# Therefore, once $v^{eff}$ is obtained, the one-body term $t^{eff}$ is then obtained by subtracting +# the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. +# Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting # from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange # correlation interactions in the active space. # -# $$t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}$$ +# .. math:: +# +# t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, # # In WEST, these parameters for the effective Hamiltonian are calculated by using the wfreq.x # executable. The program will: (i) compute the quasiparticle energies, (ii) compute the @@ -238,7 +244,7 @@ # exact removal of double counting corrections at GW level of theory, thus removing the # approximation present in the initial DFT based formulation. This formulation also helps capture # the response properties and provides access to excited state properties. Another major advantage -# of QDET is the ease with which it can be used with quantum computers in a hybrid framework[#Baker]. +# of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. # Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex # quantum systems. # diff --git a/tutorial_qdet_embedding.py b/tutorial_qdet_embedding.py deleted file mode 100644 index 99f987f2c0..0000000000 --- a/tutorial_qdet_embedding.py +++ /dev/null @@ -1,280 +0,0 @@ -r"""Quantum Defect Embedding Theory (QDET) -========================================= -Performing efficient simulations of advances materials and molecules remains a significant -challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of -available methods. However, many interesting problems in quantum chemistry and condensed matter physics -feature a strongly correlated region, which requires accurate quantum treatment, embedded within a -larger environment that could be properly treated with cheaper approximations. For example, -this is the case for point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such -as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively -addressing such problems by capturing the strong electronic correlations in the active region with high accuracy -while accounting for the environment in a more approximate manner. - -The core idea behind embedding methods is to partition the system and treat the strongly correlated -subsystem accurately, using high-level quantum mechanical methods, while approximating the effects -of the surrounding environment in a way that retains computational efficiency. In this demo, we show -how to implement the quantum defect embedding theory (QDET). The method has been successfully -applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. -An important advantage of QDET is its compatibility with quantum -algorithms as we explain in the following sections. The method can be implemented for calculating -ground and excited states, as well as dynamic properties of materials. These make QDET a -powerful method for affordable quantum simulation of materials. - -.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png - :align: center - :width: 70% - :target: javascript:void(0) - -""" - -############################################# -# Theory -# ------ -# QDET allows us to construct an effective Hamiltonian that describes the impurity -# subsystem and also accounts for the interactions between the impurity subsystem and the -# environment as -# -# .. math:: -# -# H^{eff} = \sum_{ij}^{A} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl}^{A} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, -# -# where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and -# two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. -# This Hamiltonian describes a simplified representation of the complex quantum system that is -# computationally tractable and properly captures the essential physics of the problem. The -# effective integrals :math:`t, v` are obtained -# from first-principles calculations [#Galli2]_. -# -# A QDET calculation typically starts by obtaining a meanfield approximation of the whole system -# using efficient mean field methods such as density functional theory. These calculations -# provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are -# used to construct the effective Hamiltonian which is finally solved by using either a high level -# classical method or a quantum algorithm. Let's implement these steps for an example! -# -# Implementation -# -------------- -# We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy -# defect in diamond. -# -# Mean field calculations -# ^^^^^^^^^^^^^^^^^^^^^^^ -# We use density functional theory To obtain a mean-field description of the whole system. The DFT -# calculations are performed with the QUANTUM ESPRESSO package. This requires downloading -# the pseudopotentials [#Modji]_ for each atomic species -# in the system from the QUANTUM ESPRESSO -# `database `_. We have carbon and nitrogen in -# our system which can be downloaded with -# -# .. code-block:: python -# -# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf -# wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf -# -# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` -# contains information about the system and details of the DFT calculations. More details on -# how to construct the input file can be found in QUANTUM ESPRESSO -# `documentation `_ page. -# -# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: -# -# .. code-block:: python -# -# mpirun -n 2 pw.x -i pw.in > pw.out -# -# Identify the impurity -# ^^^^^^^^^^^^^^^^^^^^^ -# Once we have obtained the meanfield description, we can identify our impurity by finding -# the states that are localized in real space around the defect region. We can identify these localized states using the -# localization factor defined as: -# -# .. math:: -# -# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 -# -# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\ohm` [#Galli2]_. -# We will use the `WEST `_ program to compute the localization factor. This requires creating another -# input file ``westpp.in`` as shown below. -# -# .. code-block:: python -# -# westpp_control: -# westpp_calculation: L # triggers the calculation of the localization factor -# westpp_range: # defines the range of states toe compute the localization factor -# - 1 # start from the first state -# - 176 # use all the 176 state -# westpp_box: # specifies the parameter of the box in atomic units for integration -# - 6.19 # -# - 10.19 -# - 6.28 -# - 10.28 -# - 6.28 -# - 10.28 -# -# We can execute this calculation as -# -# .. code-block:: python -# -# mpirun -n 2 westpp.x -i westpp.in > westpp.out -# -# This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required -# to run the calculation are large, the WEST output file needed for the next step can be -# directly downloaded as: -# -# .. code-block:: python -# -# mkdir -p west.westpp.save -# wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json -# -# We can now plot the computed localization factor for each of the states: -# -# .. code-block:: python -# -# import json -# import numpy as np -# import matplotlib.pyplot as plt -# -# with open('west.westpp.save/westpp.json','r') as f: -# data = json.load(f) -# -# y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') -# x = np.array([i+1 for i in range(y.shape[0])]) -# -# plt.plot(x,y,'o') -# plt.axhline(y=0.08,linestyle='--',color='red') -# -# plt.xlabel('KS index') -# plt.ylabel('Localization factor') -# -# plt.show() -# -# From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals -# with low and high localization factor. For the purpose of defining an impurity, we need -# highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals -# that have a localization factor > 0.06 for our active space. We'll use these orbitals for -# the calculation of the parameters for the effective Hamiltonian in the following section. -# -# Effective Hamiltonian -# ^^^^^^^^^^^^^^^^^^^^^ -# The next and probably most important steps in QDET is to define the effective one-body and -# two-body integrals for the impurity. The effective two-body integrals, :math:`v^{eff}` are computed -# first as matrix elements of the partially screened static Coulomb potential :math:`W_0^{R}`. -# -# .. math:: -# -# v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, -# -# :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, -# :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's -# polarizability. Since this leads to the inclusion of electrostatic -# and exchange-correlation effects for the active electrons, we remove these interactions from the -# the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. -# Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting -# from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange -# correlation interactions in the active space. -# -# .. math:: -# -# t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, -# -# In WEST, these parameters for the effective Hamiltonian are calculated by using the wfreq.x -# executable. The program will: (i) compute the quasiparticle energies, (ii) compute the -# partially screened Coulomb potential, and (iii) finally compute the parameters of the -# effective Hamiltonian. The input file for such a calculation is shown below: -# -# .. code-block:: python -# -# wstat_control: -# wstat_calculation: S -# n_pdep_eigen: 512 -# trev_pdep: 0.00001 -# -# wfreq_control: -# wfreq_calculation: XWGQH -# macropol_calculation: C -# l_enable_off_diagonal: true -# n_pdep_eigen_to_use: 512 -# qp_bands: [87, 122, 123, 126, 127, 128] -# n_refreq: 300 -# ecut_refreq: 2.0 -# -# We now construct the effective Hamiltonian: -# -# .. code-block:: python -# -# from westpy.qdet import QDETResult -# -# mkdir -p west.wfreq.save -# wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json -# -# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') -# -# The final step is to solve for this effective Hamiltonian using a high level method. We can -# use the WESTpy package as: -# -# .. code-block:: python -# -# solution = effective_hamiltonian.solve() -# -# We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This -# requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: -# -# .. code-block:: python -# -# from pennylane.qchem import one_particle, two_particle, observable -# import numpy as np -# -# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') -# -# one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri -# -# t = one_particle(one_e[0]) -# v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -# qubit_op = observable([t, v], mapping="jordan_wigner") -# -# The ground state energy of the Hamiltonian is identical to the one obtained before. -# -# Conclusion -# ---------- -# The quantum defect embedding theory is a novel framework for simulating strongly correlated -# quantum systems and has been successfully used for studying defects in solids. Applicability of -# QDET however is not limited to defects, it can be used for other systems where a strongly -# correlated subsystem is embedded in a weakly correlated environment. QDET is able to surpass the -# problem of correction of double counting of interactions within the active space faced by some -# other embedding theories such as DFT+DMFT. Green's function based formulation of QDET ensures -# exact removal of double counting corrections at GW level of theory, thus removing the -# approximation present in the initial DFT based formulation. This formulation also helps capture -# the response properties and provides access to excited state properties. Another major advantage -# of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. -# Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex -# quantum systems. -# -# References -# ---------- -# -# .. [#Galli] -# Joel Davidsson, Mykyta Onizhuk, *et al.*, "Discovery of atomic clock-like spin defects in simple oxides from first principles" -# `ArXiv `__. -# -# .. [#SJRLee] -# Sebastian J. R. Lee, Feizhi Ding, *et al.*, "Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding." -# `ArXiv `__. -# -# .. [#Gagliardi] -# Abhishek Mitra, Matthew Hermes, *et al.*, "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface." -# `ChemRxiv `__. -# -# .. [#Galli2] -# Nan Sheng, Christian Vorwerk, *et al.*, "Green's function formulation of quantum defect embedding theory" -# `Arxiv `__. -# -# .. [#Modji] -# Modjtaba S. Zini, Alain Delgado, *et al.*, "Quantum simulation of battery materials using ionic pseudopotentials" -# `ArXiv `__. -# -# .. [#Baker] -# Jack S. Baker, Pablo A. M. Casares, *et al.*, "Simulating optically-active spin defects with a quantum computer" -# `ArXiv `__. -# -# About the authors -# ----------------- -# From 235eabc889f7d413310faa05b53ab209a173ada7 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 13:16:02 -0400 Subject: [PATCH 26/82] Fixed metadata file --- .../tutorial_qdet_embedding.metadata.json | 49 ++++++++++++------- 1 file changed, 31 insertions(+), 18 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index be6a4707cb..407a821e17 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -1,19 +1,26 @@ { "title": "Quantum Defect Embedding Theory", - "authors": [{"username": "ddhawan"}, {"username": "soran"}], - "dateOfPublication": "2025-05-09T00:00:00+00:00", - "dateOfLastModification": "2025-05-09T00:00:00+00:00", - "categories": ["Quantum Chemistry",], + "authors": [ + { + "username": "ddhawan" + } + ], + "dateOfPublication": "2024-05-09T00:00:00+00:00", + "dateOfLastModification": "2024-05-09T00:00:00+00:00", + "categories": [ + "Quantum Chemistry", + "How-to" + ], "tags": [], "previewImages": [ { "type": "thumbnail", - "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_spin_hamiltonians.png", + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_spin_hamiltonians.png" }, { "type": "large_thumbnail", - "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_spin_hamiltonians.png", - }, + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_spin_hamiltonians.png" + } ], "seoDescription": "Learn how to build a Quantum Defect Embedding Theory (QDET) Hamiltonian.", "doi": "", @@ -23,10 +30,11 @@ "type": "article", "title": "Discovery of atomic clock-like spin defects in simple oxides from first principles", "authors": "Davidsson, Joel and Onizhuk, Mykyta and Vorwerk, Christian and Galli, Giulia", - "year": "2024", - "publisher": "", "journal": "", - "url": "https://arxiv.org/pdf/2302.07523", + "volume": "", + "pages": "", + "year": "2024", + "url": "https://arxiv.org/pdf/2302.07523" }, { "id": "SJRLee", @@ -36,7 +44,7 @@ "year": "2019", "publisher": "", "journal": "", - "url": "https://arxiv.org/pdf/1903.05830", + "url": "https://arxiv.org/pdf/1903.05830" }, { "id": "Gagliardi", @@ -46,7 +54,7 @@ "year": "2022", "publisher": "", "journal": "", - "url": "https://chemrxiv.org/engage/chemrxiv/article-details/62b0b0c40bba5d82606d2cae", + "url": "https://chemrxiv.org/engage/chemrxiv/article-details/62b0b0c40bba5d82606d2cae" }, { "id": "Galli2", @@ -56,7 +64,7 @@ "year": "2022", "publisher": "", "journal": "", - "url": "https://arxiv.org/pdf/2203.05493", + "url": "https://arxiv.org/pdf/2203.05493" }, { "id": "Modji", @@ -66,7 +74,7 @@ "year": "2023", "publisher": "", "journal": "", - "url": "https://arxiv.org/pdf/2302.07981", + "url": "https://arxiv.org/pdf/2302.07981" }, { "id": "Baker", @@ -76,12 +84,17 @@ "year": "2024", "publisher": "", "journal": "", - "url": "https://arxiv.org/pdf/2405.13115", - }, + "url": "https://arxiv.org/pdf/2405.13115" + } + ], "basedOnPapers": [], "referencedByPapers": [], "relatedContent": [ - {"type": "demonstration", "id": "tutorial_quantum_chemistry", "weight": 1.0} - ], + { + "type": "demonstration", + "id": "tutorial_quantum_chemistry", + "weight": 1.0 + } + ] } From 3f55f6a673ff0274852217e087a0fa0108356abf Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 13:25:51 -0400 Subject: [PATCH 27/82] updated metadata file --- demonstrations/tutorial_qdet_embedding.metadata.json | 3 +-- demonstrations/tutorial_qdet_embedding.py | 6 +++--- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index 407a821e17..35d78e036b 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -85,8 +85,7 @@ "publisher": "", "journal": "", "url": "https://arxiv.org/pdf/2405.13115" - } - + } ], "basedOnPapers": [], "referencedByPapers": [], diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 99f987f2c0..36c3fef423 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -265,15 +265,15 @@ # # .. [#Galli2] # Nan Sheng, Christian Vorwerk, *et al.*, "Green's function formulation of quantum defect embedding theory" -# `Arxiv `__. +# `Arxiv `__. # # .. [#Modji] # Modjtaba S. Zini, Alain Delgado, *et al.*, "Quantum simulation of battery materials using ionic pseudopotentials" -# `ArXiv `__. +# `ArXiv `__. # # .. [#Baker] # Jack S. Baker, Pablo A. M. Casares, *et al.*, "Simulating optically-active spin defects with a quantum computer" -# `ArXiv `__. +# `ArXiv `__. # # About the authors # ----------------- From b450a8f060432387b65095288a3d02bf33687118 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 9 May 2025 15:48:35 -0400 Subject: [PATCH 28/82] fixing metadata --- demonstrations/tutorial_qdet_embedding.metadata.json | 7 ------- 1 file changed, 7 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index 35d78e036b..01c5c7d28c 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -31,8 +31,6 @@ "title": "Discovery of atomic clock-like spin defects in simple oxides from first principles", "authors": "Davidsson, Joel and Onizhuk, Mykyta and Vorwerk, Christian and Galli, Giulia", "journal": "", - "volume": "", - "pages": "", "year": "2024", "url": "https://arxiv.org/pdf/2302.07523" }, @@ -42,7 +40,6 @@ "title": "Analytical gradients for projection-based wavefunction-in-DFT embedding", "authors": "Lee, Sebastian JR and Ding, Feizhi and Manby, Frederick R and Miller, Thomas F", "year": "2019", - "publisher": "", "journal": "", "url": "https://arxiv.org/pdf/1903.05830" }, @@ -52,7 +49,6 @@ "title": "Periodic density matrix embedding for co adsorption on the mgo (001) surface", "authors": "Mitra, Abhishek and Hermes, Matthew R and Cho, Minsik and Agarawal, Valay and Gagliardi, Laura", "year": "2022", - "publisher": "", "journal": "", "url": "https://chemrxiv.org/engage/chemrxiv/article-details/62b0b0c40bba5d82606d2cae" }, @@ -62,7 +58,6 @@ "title": "Green’s function formulation of quantum defect embedding theory", "authors": "Sheng, Nan and Vorwerk, Christian and Govoni, Marco and Galli, Giulia", "year": "2022", - "publisher": "", "journal": "", "url": "https://arxiv.org/pdf/2203.05493" }, @@ -72,7 +67,6 @@ "title": "Quantum simulation of battery materials using ionic pseudopotentials", "authors": "Zini, Modjtaba Shokrian and Delgado, Alain and dos Reis, Roberto and Casares, Pablo Antonio Moreno and Mueller, Jonathan E and Voigt, Arne-Christian and Arrazola, Juan Miguel", "year": "2023", - "publisher": "", "journal": "", "url": "https://arxiv.org/pdf/2302.07981" }, @@ -82,7 +76,6 @@ "title": "Simulating optically active spin defects with a quantum computer", "authors": "Baker, Jack S and Casares, Pablo AM and Zini, Modjtaba Shokrian and Thik, Jaydeep and Banerjee, Debasish and Ling, Chen and Delgado, Alain and Arrazola, Juan Miguel", "year": "2024", - "publisher": "", "journal": "", "url": "https://arxiv.org/pdf/2405.13115" } From 3a1bb7d24218c2019a0724889c0b1734700c9ab9 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 20 May 2025 20:55:35 -0400 Subject: [PATCH 29/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 36c3fef423..124b1a5f77 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,6 +1,6 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Performing efficient simulations of advances materials and molecules remains a significant +Performing efficient simulations of advanced materials and molecules remains a significant challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of available methods. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a From 1e11481ef2dc16ba1c6de29f6078e18a374c8bbd Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 11:59:31 -0400 Subject: [PATCH 30/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 124b1a5f77..d3667c4eb2 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -12,7 +12,7 @@ The core idea behind embedding methods is to partition the system and treat the strongly correlated subsystem accurately, using high-level quantum mechanical methods, while approximating the effects -of the surrounding environment in a way that retains computational efficiency. In this demo, we show +of the environment in a way that retains computational efficiency. In this demo, we show how to implement the quantum defect embedding theory (QDET). The method has been successfully applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. An important advantage of QDET is its compatibility with quantum From 8e17edc8bf55c51e68513840756f220fda32fd6e Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 11:59:47 -0400 Subject: [PATCH 31/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index d3667c4eb2..7873c1d156 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -13,7 +13,7 @@ The core idea behind embedding methods is to partition the system and treat the strongly correlated subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the environment in a way that retains computational efficiency. In this demo, we show -how to implement the quantum defect embedding theory (QDET). The method has been successfully +how to implement the quantum defect embedding theory (QDET). This method has been successfully applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. The method can be implemented for calculating From cf6ea83e6f6302fbdbd43f67a9803afdc35d5968 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:00:09 -0400 Subject: [PATCH 32/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 7873c1d156..870a81a379 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -16,7 +16,7 @@ how to implement the quantum defect embedding theory (QDET). This method has been successfully applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. An important advantage of QDET is its compatibility with quantum -algorithms as we explain in the following sections. The method can be implemented for calculating +algorithms as we explain in the following sections. It can be implemented for calculating ground and excited states, as well as dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation of materials. From bd9d75d877132353008e7eada1605ee1f46a06bd Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:00:35 -0400 Subject: [PATCH 33/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 870a81a379..a924440b7b 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -31,7 +31,7 @@ # Theory # ------ # QDET allows us to construct an effective Hamiltonian that describes the impurity -# subsystem and also accounts for the interactions between the impurity subsystem and the +# subsystem while also accounting for its interaction with the environment, as follows # environment as # # .. math:: From c815f83ec9d325d722143bf808793acf064ff48d Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:00:54 -0400 Subject: [PATCH 34/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a924440b7b..a4ded9d86f 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -46,7 +46,7 @@ # from first-principles calculations [#Galli2]_. # # A QDET calculation typically starts by obtaining a meanfield approximation of the whole system -# using efficient mean field methods such as density functional theory. These calculations +# using density functional theory. These calculations # provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are # used to construct the effective Hamiltonian which is finally solved by using either a high level # classical method or a quantum algorithm. Let's implement these steps for an example! From 50cc18d7be6c43b997c297ae63aadb75ca17ff93 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:01:07 -0400 Subject: [PATCH 35/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a4ded9d86f..a0209a39e2 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -45,7 +45,7 @@ # effective integrals :math:`t, v` are obtained # from first-principles calculations [#Galli2]_. # -# A QDET calculation typically starts by obtaining a meanfield approximation of the whole system +# A QDET calculation starts by obtaining a meanfield approximation of the whole system # using density functional theory. These calculations # provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are # used to construct the effective Hamiltonian which is finally solved by using either a high level From 2797710ac0c4502f61d6a9a21bb04eebe578b0f0 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:01:44 -0400 Subject: [PATCH 36/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a0209a39e2..aa7c3a30c4 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -58,7 +58,7 @@ # # Mean field calculations # ^^^^^^^^^^^^^^^^^^^^^^^ -# We use density functional theory To obtain a mean-field description of the whole system. The DFT +# We use density functional theory (DFT) To obtain a mean-field description of the whole system. The DFT # calculations are performed with the QUANTUM ESPRESSO package. This requires downloading # the pseudopotentials [#Modji]_ for each atomic species # in the system from the QUANTUM ESPRESSO From d284e67e0db46ad984fd15d4ba1ad9711a51cf5e Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:01:57 -0400 Subject: [PATCH 37/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index aa7c3a30c4..60248f845d 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -83,7 +83,7 @@ # # Identify the impurity # ^^^^^^^^^^^^^^^^^^^^^ -# Once we have obtained the meanfield description, we can identify our impurity by finding +# Once we have obtained the mean field description, we can identify our impurity by finding # the states that are localized in real space around the defect region. We can identify these localized states using the # localization factor defined as: # From 45761aa51b754cfd23cc29daaf3a8ef8f9ea6de4 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:02:14 -0400 Subject: [PATCH 38/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 60248f845d..dafdfdc84e 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -84,7 +84,7 @@ # Identify the impurity # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the mean field description, we can identify our impurity by finding -# the states that are localized in real space around the defect region. We can identify these localized states using the +# the states that are localized in real space around the defect region. To that end, we compute the # localization factor defined as: # # .. math:: From c253095cf863d8cd7947220e9419f73463753f6e Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:02:29 -0400 Subject: [PATCH 39/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index dafdfdc84e..137c3fbf01 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -92,7 +92,7 @@ # L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 # # where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\ohm` [#Galli2]_. -# We will use the `WEST `_ program to compute the localization factor. This requires creating another +# We will use the `WEST `_ program to compute the localization factor. This requires creating the # input file ``westpp.in`` as shown below. # # .. code-block:: python From 06d2c9d075840ba54e539e4982aa3c924fc20c8d Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:02:46 -0400 Subject: [PATCH 40/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 137c3fbf01..6888571550 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -116,7 +116,7 @@ # # mpirun -n 2 westpp.x -i westpp.in > westpp.out # -# This creates a file named ``west.westpp.save/westpp.json``. Since computational resources required +# This creates the file ``west.westpp.save/westpp.json``. Since computational resources required # to run the calculation are large, the WEST output file needed for the next step can be # directly downloaded as: # From 1ec48a4f7e056eb03559a708c0cc832d080ee277 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:03:31 -0400 Subject: [PATCH 41/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 6888571550..9638dbef21 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -165,7 +165,7 @@ # # :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, # :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's -# polarizability. Since this leads to the inclusion of electrostatic +# polarizability. Since solving the effective Hamiltonian # and exchange-correlation effects for the active electrons, we remove these interactions from the # the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. # Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting From 61248d316ff9978483c131bfb0ad792337652414 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:03:41 -0400 Subject: [PATCH 42/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 9638dbef21..391b1a48da 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -166,7 +166,7 @@ # :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, # :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's # polarizability. Since solving the effective Hamiltonian -# and exchange-correlation effects for the active electrons, we remove these interactions from the +# accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the # the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. # Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting # from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange From 325b8d9a45a986ab9661c03d64e97ffae2a257e2 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:04:13 -0400 Subject: [PATCH 43/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 391b1a48da..e6947286c4 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -168,7 +168,7 @@ # polarizability. Since solving the effective Hamiltonian # accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the # the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. -# Therefore, once :math:`v^{eff}` is obtained, the one-body term :math:`t^{eff}` is then obtained by subtracting +# Therefore, the one-body term :math:`t^{eff}` is obtained by subtracting # from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange # correlation interactions in the active space. # From 8611fc53a06181f420ed3df8188e7c4af72d7341 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:04:35 -0400 Subject: [PATCH 44/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index e6947286c4..c86dfeffd4 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -167,7 +167,7 @@ # :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's # polarizability. Since solving the effective Hamiltonian # accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the -# the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. +# the Kohn-Sham (KS) Hamiltonian, :math:`H^{KS}`, to avoid double counting them. # Therefore, the one-body term :math:`t^{eff}` is obtained by subtracting # from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange # correlation interactions in the active space. From 8e0a3298f8742f25fcf3481d0290c3e67e92b9b0 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:05:07 -0400 Subject: [PATCH 45/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index c86dfeffd4..d13b937453 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -169,7 +169,7 @@ # accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the # the Kohn-Sham (KS) Hamiltonian, :math:`H^{KS}`, to avoid double counting them. # Therefore, the one-body term :math:`t^{eff}` is obtained by subtracting -# from the Kohn-Sham Hamiltonian the term accounting for electrostatic and exchange +# from the Kohn-Sham Hamiltonian the double-counting (dc) term accounting for electrostatic and exchange- # correlation interactions in the active space. # # .. math:: From 5f03f8a280aa67a3a0ee15553e226213e1544e95 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Wed, 21 May 2025 12:05:19 -0400 Subject: [PATCH 46/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: agran2018 <45397799+agran2018@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index d13b937453..6414dc0d81 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -245,7 +245,7 @@ # approximation present in the initial DFT based formulation. This formulation also helps capture # the response properties and provides access to excited state properties. Another major advantage # of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. -# Therefore, We can conclude here that QDET is a powerful embedding approach for simulating complex +# Therefore, we can conclude here that QDET is a powerful embedding approach for simulating complex # quantum systems. # # References From 1944b4bbe298535fc092f4d273c94b5f999ab7b4 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Wed, 21 May 2025 12:17:36 -0400 Subject: [PATCH 47/82] Addressed comments --- demonstrations/tutorial_qdet_embedding.py | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 6414dc0d81..ddaf2fb54d 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -45,10 +45,10 @@ # effective integrals :math:`t, v` are obtained # from first-principles calculations [#Galli2]_. # -# A QDET calculation starts by obtaining a meanfield approximation of the whole system -# using density functional theory. These calculations -# provide a set of orbitals which can be split into impurity and bath orbitals. These orbitals are -# used to construct the effective Hamiltonian which is finally solved by using either a high level +# A QDET calculation is initiated obtaining a mean field approximation of the whole system +# using density functional theory (DFT). These calculations provide a set of orbitals +# which can be split into impurity and bath. An effective Hamiltonian is constructed from +# the impurity orbitals, which is subsequently solved by using either a high level # classical method or a quantum algorithm. Let's implement these steps for an example! # # Implementation @@ -58,7 +58,7 @@ # # Mean field calculations # ^^^^^^^^^^^^^^^^^^^^^^^ -# We use density functional theory (DFT) To obtain a mean-field description of the whole system. The DFT +# We use DFT To obtain a mean field description of the whole system. The DFT # calculations are performed with the QUANTUM ESPRESSO package. This requires downloading # the pseudopotentials [#Modji]_ for each atomic species # in the system from the QUANTUM ESPRESSO @@ -215,8 +215,10 @@ # # solution = effective_hamiltonian.solve() # -# We can also use this effective Hamiltonian with a quantum algorithm through PennyLane. This -# requires representing it in the qubit Hamiltonian format for PennyLane and can be done as follows: +# This effective Hamiltonian can be directly used with quantum algorithms in PennyLane +# once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals +# in chemists' notation, a conversion to the physicists' notation is essential for +# compatibility with PennyLane's framework. Here's how to construct the qubit Hamiltonian: # # .. code-block:: python # From 79c068206ac9eae3b78de320836aa12d4af8ed92 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Thu, 22 May 2025 09:42:29 -0400 Subject: [PATCH 48/82] Addressed some comments --- demonstrations/tutorial_qdet_embedding.py | 38 +++++++++++------------ 1 file changed, 18 insertions(+), 20 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index ddaf2fb54d..07084ffe86 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,6 +1,6 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Performing efficient simulations of advanced materials and molecules remains a significant +Performing efficient simulations of the electronic structure of advanced materials and molecules remains a significant challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of available methods. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a @@ -13,7 +13,7 @@ The core idea behind embedding methods is to partition the system and treat the strongly correlated subsystem accurately, using high-level quantum mechanical methods, while approximating the effects of the environment in a way that retains computational efficiency. In this demo, we show -how to implement the quantum defect embedding theory (QDET). This method has been successfully +how to implement quantum defect embedding theory (QDET). This method has been successfully applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. An important advantage of QDET is its compatibility with quantum algorithms as we explain in the following sections. It can be implemented for calculating @@ -32,11 +32,10 @@ # ------ # QDET allows us to construct an effective Hamiltonian that describes the impurity # subsystem while also accounting for its interaction with the environment, as follows -# environment as # # .. math:: # -# H^{eff} = \sum_{ij}^{A} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl}^{A} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, +# H^{eff} = \sum_{ij} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, # # where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and # two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. @@ -45,10 +44,10 @@ # effective integrals :math:`t, v` are obtained # from first-principles calculations [#Galli2]_. # -# A QDET calculation is initiated obtaining a mean field approximation of the whole system -# using density functional theory (DFT). These calculations provide a set of orbitals -# which can be split into impurity and bath. An effective Hamiltonian is constructed from -# the impurity orbitals, which is subsequently solved by using either a high level +# A QDET calculation is initiated obtaining a mean field approximation of the whole system, +# here we use density functional theory (DFT). These calculations provide a set of orbitals +# which can be partitioned into an impurity and a bath. An effective Hamiltonian is constructed from +# the impurity orbitals, which is subsequently solved by using either a high accuracy # classical method or a quantum algorithm. Let's implement these steps for an example! # # Implementation @@ -89,9 +88,9 @@ # # .. math:: # -# L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 +# L_n = \int_{V \in \Omega} d^3 r |\Psi_n^{KS}(r)|^2 # -# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\ohm` [#Galli2]_. +# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\Omega` [#Galli2]_. # We will use the `WEST `_ program to compute the localization factor. This requires creating the # input file ``westpp.in`` as shown below. # @@ -99,9 +98,9 @@ # # westpp_control: # westpp_calculation: L # triggers the calculation of the localization factor -# westpp_range: # defines the range of states toe compute the localization factor +# westpp_range: # defines the range of states to compute the localization factor # - 1 # start from the first state -# - 176 # use all the 176 state +# - 176 # use all 176 states # westpp_box: # specifies the parameter of the box in atomic units for integration # - 6.19 # # - 10.19 @@ -166,7 +165,7 @@ # :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, # :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's # polarizability. Since solving the effective Hamiltonian -# accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the +# accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the # the Kohn-Sham (KS) Hamiltonian, :math:`H^{KS}`, to avoid double counting them. # Therefore, the one-body term :math:`t^{eff}` is obtained by subtracting # from the Kohn-Sham Hamiltonian the double-counting (dc) term accounting for electrostatic and exchange- @@ -176,7 +175,7 @@ # # t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, # -# In WEST, these parameters for the effective Hamiltonian are calculated by using the wfreq.x +# In WEST, these parameters for the effective Hamiltonian are calculated by using the ``wfreq.x`` # executable. The program will: (i) compute the quasiparticle energies, (ii) compute the # partially screened Coulomb potential, and (iii) finally compute the parameters of the # effective Hamiltonian. The input file for such a calculation is shown below: @@ -237,18 +236,17 @@ # # Conclusion # ---------- -# The quantum defect embedding theory is a novel framework for simulating strongly correlated +# Quantum defect embedding theory is a novel framework for simulating strongly correlated # quantum systems and has been successfully used for studying defects in solids. Applicability of # QDET however is not limited to defects, it can be used for other systems where a strongly -# correlated subsystem is embedded in a weakly correlated environment. QDET is able to surpass the -# problem of correction of double counting of interactions within the active space faced by some -# other embedding theories such as DFT+DMFT. Green's function based formulation of QDET ensures +# correlated subsystem is embedded in a weakly correlated environment. Additionally, QDET is able to +# correct the interaction double counting issue within the active space faced by a variety of +# other embedding theories such as DFT+DMFT. The Green's function based formulation of QDET ensures # exact removal of double counting corrections at GW level of theory, thus removing the # approximation present in the initial DFT based formulation. This formulation also helps capture # the response properties and provides access to excited state properties. Another major advantage # of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. -# Therefore, we can conclude here that QDET is a powerful embedding approach for simulating complex -# quantum systems. +# In conclusion, QDET is a powerful embedding approach for simulating complex quantum systems. # # References # ---------- From 85a4a7f8951e1a14a81f4f819c5a8f307ba3fd5b Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Thu, 22 May 2025 15:54:49 -0400 Subject: [PATCH 49/82] Fixed some errors --- demonstrations/tutorial_qdet_embedding.py | 40 ++++++++++++----------- 1 file changed, 21 insertions(+), 19 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 07084ffe86..a7ec82a3ac 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -64,7 +64,7 @@ # `database `_. We have carbon and nitrogen in # our system which can be downloaded with # -# .. code-block:: python +# .. code-block:: bash # # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf @@ -76,7 +76,7 @@ # # We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: # -# .. code-block:: python +# .. code-block:: bash # # mpirun -n 2 pw.x -i pw.in > pw.out # @@ -94,7 +94,7 @@ # We will use the `WEST `_ program to compute the localization factor. This requires creating the # input file ``westpp.in`` as shown below. # -# .. code-block:: python +# .. code-block:: text # # westpp_control: # westpp_calculation: L # triggers the calculation of the localization factor @@ -111,7 +111,7 @@ # # We can execute this calculation as # -# .. code-block:: python +# .. code-block:: bash # # mpirun -n 2 westpp.x -i westpp.in > westpp.out # @@ -119,7 +119,7 @@ # to run the calculation are large, the WEST output file needed for the next step can be # directly downloaded as: # -# .. code-block:: python +# .. code-block:: bash # # mkdir -p west.westpp.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json @@ -180,31 +180,33 @@ # partially screened Coulomb potential, and (iii) finally compute the parameters of the # effective Hamiltonian. The input file for such a calculation is shown below: # -# .. code-block:: python +# .. code-block:: text # # wstat_control: -# wstat_calculation: S -# n_pdep_eigen: 512 -# trev_pdep: 0.00001 +# wstat_calculation: S #starts the calculation from scratch +# n_pdep_eigen: 512 #number of PDEP eigenpotentials, set to match the number of electrons +# trev_pdep: 0.00001 #convergence threshold for PDEP eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH -# macropol_calculation: C -# l_enable_off_diagonal: true -# n_pdep_eigen_to_use: 512 -# qp_bands: [87, 122, 123, 126, 127, 128] -# n_refreq: 300 -# ecut_refreq: 2.0 +# wfreq_calculation: XWGQH # compute the quasiparticle corrections and :math:H^{eff} parameters +# macropol_calculation: C # include long-wavelength limit for condensed systems +# l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy +# n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used +# qp_bands: [87, 122, 123, 126, 127, 128] # impurity orbitals +# n_refreq: 300 # number of frequencies on the real axis +# ecut_refreq: 2.0 # cutoff for the real frequencies # # We now construct the effective Hamiltonian: # -# .. code-block:: python -# -# from westpy.qdet import QDETResult +# .. code-block:: bash # # mkdir -p west.wfreq.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json # +# .. code-block:: python +# +# from westpy.qdet import QDETResult +# # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') # # The final step is to solve for this effective Hamiltonian using a high level method. We can From f3eb553a9453ca2eb54b7ac356530b6f73334892 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Thu, 22 May 2025 17:59:41 -0400 Subject: [PATCH 50/82] Testing rendering --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a7ec82a3ac..212e357e2a 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -188,7 +188,7 @@ # trev_pdep: 0.00001 #convergence threshold for PDEP eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH # compute the quasiparticle corrections and :math:H^{eff} parameters +# wfreq_calculation: XWGQH # compute the quasiparticle corrections and $H^{eff}$ parameters # macropol_calculation: C # include long-wavelength limit for condensed systems # l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy # n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used From fc9f82c12fbb03c59da11604a88218d9f894e880 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 23 May 2025 09:20:28 -0400 Subject: [PATCH 51/82] Added plot --- .../qdet_data/west.westpp.save/westpp.json | 1 + demonstrations/tutorial_qdet_embedding.py | 40 +++++++++---------- 2 files changed, 20 insertions(+), 21 deletions(-) create mode 100644 demonstrations/qdet_data/west.westpp.save/westpp.json diff --git a/demonstrations/qdet_data/west.westpp.save/westpp.json b/demonstrations/qdet_data/west.westpp.save/westpp.json new file mode 100644 index 0000000000..f97edfcf88 --- /dev/null +++ b/demonstrations/qdet_data/west.westpp.save/westpp.json @@ -0,0 +1 @@ +{"runjob":{"startdate":" 2Feb2024","starttime":"21: 2:16","completed":true,"endtime":"21: 2:19","enddate":" 2Feb2024"},"software":{"package":"WEST","program":"WESTPP","version":"5.5.0","westgit":"v5.5.0-90-ge2a5c01","website":"https://west-code.org","citation":"M. Govoni et al., J. Chem. Theory Comput. 11, 2680 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b/demonstrations/tutorial_qdet_embedding.py index 212e357e2a..8878648968 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -126,25 +126,23 @@ # # We can now plot the computed localization factor for each of the states: # -# .. code-block:: python -# -# import json -# import numpy as np -# import matplotlib.pyplot as plt -# -# with open('west.westpp.save/westpp.json','r') as f: -# data = json.load(f) -# -# y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') -# x = np.array([i+1 for i in range(y.shape[0])]) -# -# plt.plot(x,y,'o') -# plt.axhline(y=0.08,linestyle='--',color='red') -# -# plt.xlabel('KS index') -# plt.ylabel('Localization factor') -# -# plt.show() +import json +import numpy as np +import matplotlib.pyplot as plt + +with open('qdet_data/west.westpp.save/westpp.json','r') as f: + data = json.load(f) + +y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') +x = np.array([i+1 for i in range(y.shape[0])]) + +plt.plot(x,y,'o') +plt.axhline(y=0.08,linestyle='--',color='red') + +plt.xlabel('KS index') +plt.ylabel('Localization factor') + +plt.show() # # From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals # with low and high localization factor. For the purpose of defining an impurity, we need @@ -210,13 +208,13 @@ # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') # # The final step is to solve for this effective Hamiltonian using a high level method. We can -# use the WESTpy package as: +# use the FCI algorithm from WESTpy package as: # # .. code-block:: python # # solution = effective_hamiltonian.solve() # -# This effective Hamiltonian can be directly used with quantum algorithms in PennyLane +# This effective Hamiltonian can also be directly used with quantum algorithms in PennyLane # once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals # in chemists' notation, a conversion to the physicists' notation is essential for # compatibility with PennyLane's framework. Here's how to construct the qubit Hamiltonian: From bb5300a2633ddf14ded354b08f45f32d8f4be046 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 23 May 2025 09:53:10 -0400 Subject: [PATCH 52/82] Added plot --- demonstrations/qdet_data/localization.jpeg | Bin 0 -> 23621 bytes .../qdet_data/west.westpp.save/westpp.json | 1 - demonstrations/tutorial_qdet_embedding.py | 57 +++++++++++------- 3 files changed, 36 insertions(+), 22 deletions(-) create mode 100644 demonstrations/qdet_data/localization.jpeg delete mode 100644 demonstrations/qdet_data/west.westpp.save/westpp.json diff --git a/demonstrations/qdet_data/localization.jpeg b/demonstrations/qdet_data/localization.jpeg new file mode 100644 index 0000000000000000000000000000000000000000..f34af6316ae4425125b33ace45fdbb1b1d368ae1 GIT binary patch literal 23621 zcmeIa1yr2NmNwkDYk=U800DvpcXtTx9xO-)2yVeGxI=JvXx!c1HMqOG^YuCBo;!EW z%$=F<%FO?-Z<4s|s=aIPXYYDySG~-=tOC%b#3aQ45D*XmBk&*KWdR@zfQN;J 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b/demonstrations/tutorial_qdet_embedding.py index 8878648968..49c7d09cc5 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -126,25 +126,33 @@ # # We can now plot the computed localization factor for each of the states: # -import json -import numpy as np -import matplotlib.pyplot as plt +# .. code-block:: bash +# +# import json +# import numpy as np +# import matplotlib.pyplot as plt -with open('qdet_data/west.westpp.save/westpp.json','r') as f: - data = json.load(f) +# with open('west.westpp.save/westpp.json','r') as f: +# data = json.load(f) -y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') -x = np.array([i+1 for i in range(y.shape[0])]) +# y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') +# x = np.array([i+1 for i in range(y.shape[0])]) -plt.plot(x,y,'o') -plt.axhline(y=0.08,linestyle='--',color='red') +# plt.plot(x,y,'o') +# plt.axhline(y=0.08,linestyle='--',color='red') -plt.xlabel('KS index') -plt.ylabel('Localization factor') +# plt.xlabel('KS index') +# plt.ylabel('Localization factor') -plt.show() +# plt.show() +# # -# From this plot, it is easy to see that Kohn-Sham orbitals can be catergorized as orbitals +# .. figure:: qdet_data/localization.jpeg +# :align: center +# :width: 70% +# :target: javascript:void(0) +# +# From this plot, it is easy to see that Kohn-Sham orbitals can be categorized as orbitals # with low and high localization factor. For the purpose of defining an impurity, we need # highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals # that have a localization factor > 0.06 for our active space. We'll use these orbitals for @@ -186,21 +194,28 @@ # trev_pdep: 0.00001 #convergence threshold for PDEP eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH # compute the quasiparticle corrections and $H^{eff}$ parameters -# macropol_calculation: C # include long-wavelength limit for condensed systems -# l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy -# n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used -# qp_bands: [87, 122, 123, 126, 127, 128] # impurity orbitals -# n_refreq: 300 # number of frequencies on the real axis -# ecut_refreq: 2.0 # cutoff for the real frequencies +# wfreq_calculation: XWGQH # compute the quasiparticle corrections and $H^{eff}$ parameters +# macropol_calculation: C # include long-wavelength limit for condensed systems +# l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy +# n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used +# qp_bands: [87,122,123,126,127,128] # impurity orbitals +# n_refreq: 300 # number of frequencies on the real axis +# ecut_refreq: 2.0 # cutoff for the real frequencies +# +# We can execute this calculation as follows: +# .. code-block:: bash # -# We now construct the effective Hamiltonian: +# mpirun -n 2 wfreq.x -i wfreq.in > wfreq.out +# +# This calculation takes some time and requires computational resources, therefore the output file can be downloaded as # # .. code-block:: bash # # mkdir -p west.wfreq.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json # +# We now construct the effective Hamiltonian by importing the results from above file: +# # .. code-block:: python # # from westpy.qdet import QDETResult From 651d0d72e38f22de8c3046c3581ba81350599d99 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Fri, 23 May 2025 10:11:49 -0400 Subject: [PATCH 53/82] Addressed all comments --- demonstrations/qdet_data/localization.jpeg | Bin 23621 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a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -72,7 +72,12 @@ # Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` # contains information about the system and details of the DFT calculations. More details on # how to construct the input file can be found in QUANTUM ESPRESSO -# `documentation `_ page. +# `documentation `_ page. For the system taken here, +# the input file can be downloaded with +# +# .. code-block:: bash +# +# wget -N -q https://west-code.org/doc/training/nv_diamond_63/pw.in # # We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: # @@ -84,7 +89,7 @@ # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the mean field description, we can identify our impurity by finding # the states that are localized in real space around the defect region. To that end, we compute the -# localization factor defined as: +# localization factor for each state n, defined as: # # .. math:: # @@ -147,7 +152,7 @@ # plt.show() # # -# .. figure:: qdet_data/localization.jpeg +# .. figure:: ../_static/demonstration_assets/qdet/localization.jpeg # :align: center # :width: 70% # :target: javascript:void(0) @@ -194,7 +199,7 @@ # trev_pdep: 0.00001 #convergence threshold for PDEP eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH # compute the quasiparticle corrections and $H^{eff}$ parameters +# wfreq_calculation: XWGQH # compute the quasiparticle corrections and :math:`H^{eff}` parameters # macropol_calculation: C # include long-wavelength limit for condensed systems # l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy # n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used @@ -229,6 +234,8 @@ # # solution = effective_hamiltonian.solve() # +# The solution object is a dictionary containing information about the FCI eigenstates of the system, which +# includes the various excitation energies, spin multiplicities, eigenvectors etc. # This effective Hamiltonian can also be directly used with quantum algorithms in PennyLane # once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals # in chemists' notation, a conversion to the physicists' notation is essential for @@ -247,7 +254,8 @@ # v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) # qubit_op = observable([t, v], mapping="jordan_wigner") # -# The ground state energy of the Hamiltonian is identical to the one obtained before. +# We can compare the energies obtained from the diagnolization of this qubit Hamiltonian to the +# solution object above to see that they match. # # Conclusion # ---------- From e715a9ed1ac0b0e7fc1ae3e56db69b852426dc52 Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 29 May 2025 10:26:03 -0400 Subject: [PATCH 54/82] update text --- demonstrations/tutorial_qdet_embedding.py | 64 +++++++++++------------ 1 file changed, 31 insertions(+), 33 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 1f0c4baccd..b7fbda748f 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,24 +1,22 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Performing efficient simulations of the electronic structure of advanced materials and molecules remains a significant -challenge in quantum chemistry and condensed matter physics due to the prohibitive costs of -available methods. However, many interesting problems in quantum chemistry and condensed matter physics -feature a strongly correlated region, which requires accurate quantum treatment, embedded within a -larger environment that could be properly treated with cheaper approximations. For example, -this is the case for point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such -as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively -addressing such problems by capturing the strong electronic correlations in the active region with high accuracy -while accounting for the environment in a more approximate manner. +Performing efficient simulations of the electronic structure of materials and molecules remains a +significant challenge due to the prohibitive costs of available classical methods. However, many +interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated +region, which requires accurate quantum treatment, embedded within a larger environment that could +be properly treated with cheaper approximations. For example, point defects in materials [#Galli]_, +active site of catalysts [#SJRLee]_, surface phenomenon such as adsorption [#Gagliardi]_ and many +more. Embedding theories serve as powerful tools for effectively addressing such problems by +capturing the strong electronic correlations in the active region with high accuracy while +accounting for the environment in a more approximate manner. -The core idea behind embedding methods is to partition the system and treat the strongly correlated -subsystem accurately, using high-level quantum mechanical methods, while approximating the effects -of the environment in a way that retains computational efficiency. In this demo, we show -how to implement quantum defect embedding theory (QDET). This method has been successfully -applied to study defects in CaO [#Galli]_ and to calculate excitations of the negatively charged NV center in diamond [#Galli2]_. -An important advantage of QDET is its compatibility with quantum -algorithms as we explain in the following sections. It can be implemented for calculating -ground and excited states, as well as dynamic properties of materials. These make QDET a -powerful method for affordable quantum simulation of materials. +In this demo, we show how to implement quantum defect embedding theory (QDET) [#Galli]_. This method +has been successfully applied to study systems such as defects in CaO [#Galli]_ and to calculate +excitations of the negatively charged nitrogen-vacancy defect in diamond [#Galli2]_. QDET can be implemented for +calculating both ground and excited states as well as dynamic properties of materials. These make +QDET a powerful method for affordable quantum simulation of materials. Another important advantage +of QDET is the compatibility of the method with quantum algorithms as we explain in the following +sections. .. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png :align: center @@ -30,7 +28,7 @@ ############################################# # Theory # ------ -# QDET allows us to construct an effective Hamiltonian that describes the impurity +# The QDET method allows us to construct an effective Hamiltonian that describes the impurity # subsystem while also accounting for its interaction with the environment, as follows # # .. math:: @@ -41,14 +39,14 @@ # two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. # This Hamiltonian describes a simplified representation of the complex quantum system that is # computationally tractable and properly captures the essential physics of the problem. The -# effective integrals :math:`t, v` are obtained -# from first-principles calculations [#Galli2]_. +# effective integrals :math:`t, v` are obtained from first-principles calculations [#Galli2]_. # -# A QDET calculation is initiated obtaining a mean field approximation of the whole system, -# here we use density functional theory (DFT). These calculations provide a set of orbitals -# which can be partitioned into an impurity and a bath. An effective Hamiltonian is constructed from -# the impurity orbitals, which is subsequently solved by using either a high accuracy -# classical method or a quantum algorithm. Let's implement these steps for an example! +# A QDET simulation typically starts by obtaining a meanfield approximation of the whole system +# using efficient quantum chemistry methods such as density functional theory (DFT). These +# calculations provide a set of orbitals which can be partitioned into impurity and bath orbitals. +# The effective Hamiltonian is constructed from the impurity orbitals, which is subsequently solved +# by using either a high accuracy classical method or a quantum algorithm. Let's implement these +# steps for an example! # # Implementation # -------------- @@ -136,19 +134,19 @@ # import json # import numpy as np # import matplotlib.pyplot as plt - +# # with open('west.westpp.save/westpp.json','r') as f: # data = json.load(f) - +# # y = np.array(data['output']['L']['K000001']['local_factor'],dtype='f8') # x = np.array([i+1 for i in range(y.shape[0])]) - +# # plt.plot(x,y,'o') # plt.axhline(y=0.08,linestyle='--',color='red') - +# # plt.xlabel('KS index') # plt.ylabel('Localization factor') - +# # plt.show() # # @@ -243,7 +241,7 @@ # # .. code-block:: python # -# from pennylane.qchem import one_particle, two_particle, observable +# #from pennylane.qchem import one_particle, two_particle, observable # import numpy as np # # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') @@ -252,7 +250,7 @@ # # t = one_particle(one_e[0]) # v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -# qubit_op = observable([t, v], mapping="jordan_wigner") +# #qubit_op = observable([t, v], mapping="jordan_wigner") # # We can compare the energies obtained from the diagnolization of this qubit Hamiltonian to the # solution object above to see that they match. From 4d372872342e89a9e1174541840f6f1d0bf88001 Mon Sep 17 00:00:00 2001 From: soranjh Date: Thu, 29 May 2025 11:47:04 -0400 Subject: [PATCH 55/82] update text --- demonstrations/tutorial_qdet_embedding.py | 93 ++++++++++++----------- 1 file changed, 47 insertions(+), 46 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index b7fbda748f..cd84169a17 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -41,33 +41,30 @@ # computationally tractable and properly captures the essential physics of the problem. The # effective integrals :math:`t, v` are obtained from first-principles calculations [#Galli2]_. # +# Implementation +# -------------- # A QDET simulation typically starts by obtaining a meanfield approximation of the whole system # using efficient quantum chemistry methods such as density functional theory (DFT). These # calculations provide a set of orbitals which can be partitioned into impurity and bath orbitals. # The effective Hamiltonian is constructed from the impurity orbitals, which is subsequently solved # by using either a high accuracy classical method or a quantum algorithm. Let's implement these -# steps for an example! -# -# Implementation -# -------------- -# We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy -# defect in diamond. +# steps for an example! We implement QDET to compute the excitation energies of a negatively charged +# nitrogen-vacancy defect in diamond [#Galli2]_. # # Mean field calculations # ^^^^^^^^^^^^^^^^^^^^^^^ -# We use DFT To obtain a mean field description of the whole system. The DFT -# calculations are performed with the QUANTUM ESPRESSO package. This requires downloading -# the pseudopotentials [#Modji]_ for each atomic species -# in the system from the QUANTUM ESPRESSO -# `database `_. We have carbon and nitrogen in -# our system which can be downloaded with +# We use DFT to obtain a mean field description of the whole system. The DFT +# calculations are performed with the `QUANTUM ESPRESSO `_ +# package. This requires downloading pseudopotentials [#Modji]_ for each atomic species +# in the system from the QUANTUM ESPRESSO `database `_. +# We have carbon and nitrogen in our system for which we can download pseudopotentials with # # .. code-block:: bash # # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf # -# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file ``pw.in`` +# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file # contains information about the system and details of the DFT calculations. More details on # how to construct the input file can be found in QUANTUM ESPRESSO # `documentation `_ page. For the system taken here, @@ -77,7 +74,8 @@ # # wget -N -q https://west-code.org/doc/training/nv_diamond_63/pw.in # -# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file: +# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file +# ``pw.in`` and save the results in ``pw.out``. # # .. code-block:: bash # @@ -87,15 +85,15 @@ # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the mean field description, we can identify our impurity by finding # the states that are localized in real space around the defect region. To that end, we compute the -# localization factor for each state n, defined as: +# localization factor :math:`L_n` for each state ``n``, defined as: # # .. math:: # # L_n = \int_{V \in \Omega} d^3 r |\Psi_n^{KS}(r)|^2 # # where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\Omega` [#Galli2]_. -# We will use the `WEST `_ program to compute the localization factor. This requires creating the -# input file ``westpp.in`` as shown below. +# We will use the `WEST `_ program to compute the +# localization factor. This requires creating the input file ``westpp.in`` as shown below. # # .. code-block:: text # @@ -105,22 +103,22 @@ # - 1 # start from the first state # - 176 # use all 176 states # westpp_box: # specifies the parameter of the box in atomic units for integration -# - 6.19 # +# - 6.19 # - 10.19 # - 6.28 # - 10.28 # - 6.28 # - 10.28 # -# We can execute this calculation as +# We can now perform the calculation with # # .. code-block:: bash # # mpirun -n 2 westpp.x -i westpp.in > westpp.out # -# This creates the file ``west.westpp.save/westpp.json``. Since computational resources required -# to run the calculation are large, the WEST output file needed for the next step can be -# directly downloaded as: +# This creates the file ``westpp.json`` which contains the information we need here. Since +# computational resources required to run the calculation are large, we just download a pre-computed +# file with: # # .. code-block:: bash # @@ -155,30 +153,31 @@ # :width: 70% # :target: javascript:void(0) # -# From this plot, it is easy to see that Kohn-Sham orbitals can be categorized as orbitals -# with low and high localization factor. For the purpose of defining an impurity, we need +# From this plot, it is easy to see that the Kohn-Sham orbitals can be categorized as orbitals +# with low and high localization factors. For the purpose of defining an impurity, we need # highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals -# that have a localization factor > 0.06 for our active space. We'll use these orbitals for -# the calculation of the parameters for the effective Hamiltonian in the following section. +# that have a localization factor > 0.06. We'll use these orbitals for the calculation of the +# parameters for the effective Hamiltonian in the following section. # # Effective Hamiltonian # ^^^^^^^^^^^^^^^^^^^^^ -# The next and probably most important steps in QDET is to define the effective one-body and -# two-body integrals for the impurity. The effective two-body integrals, :math:`v^{eff}` are computed -# first as matrix elements of the partially screened static Coulomb potential :math:`W_0^{R}`. +# The next step in QDET is to define the effective one-body and two-body integrals for the impurity. +# The effective two-body integrals, :math:`v^{eff}` are computed first as matrix elements of the +# partially screened static Coulomb potential :math:`W_0^{R}`. # # .. math:: # # v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, # -# :math:`W_0^R`, results from screening the bare Coulomb potential, :math:`v`, with the reduced polarizability, -# :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and :math:`P_{imp}` is the impurity's -# polarizability. Since solving the effective Hamiltonian -# accounts for the exchange and correlation interactions between the active electrons, we remove these interactions from the -# the Kohn-Sham (KS) Hamiltonian, :math:`H^{KS}`, to avoid double counting them. -# Therefore, the one-body term :math:`t^{eff}` is obtained by subtracting -# from the Kohn-Sham Hamiltonian the double-counting (dc) term accounting for electrostatic and exchange- -# correlation interactions in the active space. +# where :math:`W_0^R` results from screening the bare Coulomb potential, :math:`v`, with the reduced +# polarizability, :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and +# :math:`P_{imp}` is the impurity's polarizability. Since solving the effective Hamiltonian +# accounts for the exchange and correlation interactions between the active electrons, we remove +# these interactions from the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. +# +# The one-body term :math:`t^{eff}` is obtained by subtracting from the Kohn-Sham Hamiltonian the +# double-counting term accounting for electrostatic and exchange-correlation interactions in the +# active space. # # .. math:: # @@ -210,14 +209,15 @@ # # mpirun -n 2 wfreq.x -i wfreq.in > wfreq.out # -# This calculation takes some time and requires computational resources, therefore the output file can be downloaded as +# This calculation takes some time and requires computational resources, therefore we download a +# pre-computed output file with # # .. code-block:: bash # # mkdir -p west.wfreq.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json # -# We now construct the effective Hamiltonian by importing the results from above file: +# We now construct the effective Hamiltonian by importing the results from this file: # # .. code-block:: python # @@ -232,8 +232,9 @@ # # solution = effective_hamiltonian.solve() # -# The solution object is a dictionary containing information about the FCI eigenstates of the system, which -# includes the various excitation energies, spin multiplicities, eigenvectors etc. +# The solution object is a dictionary containing information about the FCI eigenstates of the +# system, which includes the various excitation energies, spin multiplicities, eigenvectors etc. +# # This effective Hamiltonian can also be directly used with quantum algorithms in PennyLane # once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals # in chemists' notation, a conversion to the physicists' notation is essential for @@ -241,7 +242,7 @@ # # .. code-block:: python # -# #from pennylane.qchem import one_particle, two_particle, observable +# from pennylane.qchem import one_particle, two_particle, observable # import numpy as np # # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') @@ -250,7 +251,7 @@ # # t = one_particle(one_e[0]) # v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -# #qubit_op = observable([t, v], mapping="jordan_wigner") +# qubit_op = observable([t, v], mapping="jordan_wigner") # # We can compare the energies obtained from the diagnolization of this qubit Hamiltonian to the # solution object above to see that they match. @@ -262,9 +263,9 @@ # QDET however is not limited to defects, it can be used for other systems where a strongly # correlated subsystem is embedded in a weakly correlated environment. Additionally, QDET is able to # correct the interaction double counting issue within the active space faced by a variety of -# other embedding theories such as DFT+DMFT. The Green's function based formulation of QDET ensures -# exact removal of double counting corrections at GW level of theory, thus removing the -# approximation present in the initial DFT based formulation. This formulation also helps capture +# other embedding theories. The Green's function based formulation of QDET ensures +# exact removal of double counting corrections at GW level of theory, thus removing the +# approximation present in the initial DFT based formulation. This formulation also helps to capture # the response properties and provides access to excited state properties. Another major advantage # of QDET is the ease with which it can be used with quantum computers in a hybrid framework [#Baker]_. # In conclusion, QDET is a powerful embedding approach for simulating complex quantum systems. 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zq(KhIz0nXt7%*4~LYXJ?e}?XbyMMtpxRr%D1h6@URZDMLPQ(czfAE5y3hcj+$$-6L z@&B27gdsZr@0Som?Ef1D!vx*^e^xqZf&b6wgNm~JzcCt7M#%qJtl(z&|1*N&(I)?I mOaZj6{%4u||9Gi^f8blYLFuCQgkt|)TTV(zvPRq_^#1{dW=8D* literal 0 HcmV?d00001 diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index cd84169a17..ce582332f3 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -18,7 +18,7 @@ of QDET is the compatibility of the method with quantum algorithms as we explain in the following sections. -.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_how_to_build_spin_hamiltonians.png +.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_qdet_embedding.png :align: center :width: 70% :target: javascript:void(0) @@ -26,8 +26,6 @@ """ ############################################# -# Theory -# ------ # The QDET method allows us to construct an effective Hamiltonian that describes the impurity # subsystem while also accounting for its interaction with the environment, as follows # @@ -217,7 +215,9 @@ # mkdir -p west.wfreq.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json # -# We now construct the effective Hamiltonian by importing the results from this file: +# Effective Hamiltonian +# ^^^^^^^^^^^^^^^^^^^^^ +# We now construct the effective Hamiltonian by importing the electron integral results: # # .. code-block:: python # @@ -225,8 +225,8 @@ # # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') # -# The final step is to solve for this effective Hamiltonian using a high level method. We can -# use the FCI algorithm from WESTpy package as: +# We can solve for this effective Hamiltonian using a high level method such as the FCI algorithm +# from WESTpy package as: # # .. code-block:: python # @@ -235,8 +235,8 @@ # The solution object is a dictionary containing information about the FCI eigenstates of the # system, which includes the various excitation energies, spin multiplicities, eigenvectors etc. # -# This effective Hamiltonian can also be directly used with quantum algorithms in PennyLane -# once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals +# More importantly, this effective Hamiltonian can also be directly used with quantum algorithms in +# PennyLane once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals # in chemists' notation, a conversion to the physicists' notation is essential for # compatibility with PennyLane's framework. Here's how to construct the qubit Hamiltonian: # From 09b32294f4037072454b653967dcb9f31bd9461d Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 11:26:10 -0400 Subject: [PATCH 58/82] update implementation --- demonstrations/tutorial_qdet_embedding.py | 126 ++++++++++++---------- 1 file changed, 71 insertions(+), 55 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index ce582332f3..7aa8070aab 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,14 +1,14 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Performing efficient simulations of the electronic structure of materials and molecules remains a +Efficient simulation of the electronic structure of materials and molecules remains a significant challenge due to the prohibitive costs of available classical methods. However, many interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated region, which requires accurate quantum treatment, embedded within a larger environment that could -be properly treated with cheaper approximations. For example, point defects in materials [#Galli]_, -active site of catalysts [#SJRLee]_, surface phenomenon such as adsorption [#Gagliardi]_ and many -more. Embedding theories serve as powerful tools for effectively addressing such problems by -capturing the strong electronic correlations in the active region with high accuracy while -accounting for the environment in a more approximate manner. +be properly treated with cheaper approximations. Example of such systems include point defects in +materials [#Galli]_, active site of catalysts [#SJRLee]_ and surface phenomenon such as adsorption +[#Gagliardi]_. Such systems can be accurately simulated with embedding theories which effectively +capture the strong electronic correlations in the active region with high accuracy while accounting +for the environment in a more approximate manner. In this demo, we show how to implement quantum defect embedding theory (QDET) [#Galli]_. This method has been successfully applied to study systems such as defects in CaO [#Galli]_ and to calculate @@ -26,8 +26,10 @@ """ ############################################# -# The QDET method allows us to construct an effective Hamiltonian that describes the impurity -# subsystem while also accounting for its interaction with the environment, as follows +# The main component of a QDET simulation is to construct an effective Hamiltonian that describes +# the impurity subsystem and its interaction with the environment. In second quantization, the +# effective Hamiltonian can be represented in terms of electronic creation, :math:`a^{\dagger}`, and +# annihilation , :math:`a`, operators as # # .. math:: # @@ -36,44 +38,42 @@ # where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and # two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. # This Hamiltonian describes a simplified representation of the complex quantum system that is -# computationally tractable and properly captures the essential physics of the problem. The -# effective integrals :math:`t, v` are obtained from first-principles calculations [#Galli2]_. +# computationally tractable while it properly captures the essential physics of the problem. # # Implementation # -------------- # A QDET simulation typically starts by obtaining a meanfield approximation of the whole system # using efficient quantum chemistry methods such as density functional theory (DFT). These -# calculations provide a set of orbitals which can be partitioned into impurity and bath orbitals. -# The effective Hamiltonian is constructed from the impurity orbitals, which is subsequently solved +# calculations provide a set of orbitals that are partitioned into impurity and bath orbitals. +# The effective Hamiltonian is constructed from the impurity orbitals and is subsequently solved # by using either a high accuracy classical method or a quantum algorithm. Let's implement these -# steps for an example! We implement QDET to compute the excitation energies of a negatively charged -# nitrogen-vacancy defect in diamond [#Galli2]_. +# steps for an example! # # Mean field calculations # ^^^^^^^^^^^^^^^^^^^^^^^ -# We use DFT to obtain a mean field description of the whole system. The DFT -# calculations are performed with the `QUANTUM ESPRESSO `_ +# We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy +# defect in diamond [#Galli2]_. We use DFT to obtain a mean field description of the whole system. +# The DFT calculations are performed with the `QUANTUM ESPRESSO `_ # package. This requires downloading pseudopotentials [#Modji]_ for each atomic species # in the system from the QUANTUM ESPRESSO `database `_. -# We have carbon and nitrogen in our system for which we can download pseudopotentials with +# We have carbon and nitrogen in our system and download their pseudopotentials with # # .. code-block:: bash # # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf # -# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file -# contains information about the system and details of the DFT calculations. More details on -# how to construct the input file can be found in QUANTUM ESPRESSO -# `documentation `_ page. For the system taken here, -# the input file can be downloaded with +# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file contains +# information about the system and the DFT calculations. More details on how to construct the input +# file can be found in QUANTUM ESPRESSO `documentation `_ +# page. For the system taken here, the input file can be downloaded with # # .. code-block:: bash # # wget -N -q https://west-code.org/doc/training/nv_diamond_63/pw.in # -# We can now perform the DFT calculations by running the executable code ``pw.x`` on the input file -# ``pw.in`` and save the results in ``pw.out``. +# We can now perform the DFT calculations by running ``pw.x`` on the input file ``pw.in`` and save +# the results in ``pw.out``. # # .. code-block:: bash # @@ -82,16 +82,17 @@ # Identify the impurity # ^^^^^^^^^^^^^^^^^^^^^ # Once we have obtained the mean field description, we can identify our impurity by finding -# the states that are localized in real space around the defect region. To that end, we compute the +# the states that are localized around the defect region in real space. To do that, we compute the # localization factor :math:`L_n` for each state ``n``, defined as: # # .. math:: # # L_n = \int_{V \in \Omega} d^3 r |\Psi_n^{KS}(r)|^2 # -# where :math:`V` is the identified volume including the impurity within the supercell volume :math:`\Omega` [#Galli2]_. -# We will use the `WEST `_ program to compute the -# localization factor. This requires creating the input file ``westpp.in`` as shown below. +# where :math:`V` is the identified volume including the impurity within the supercell volume +# :math:`\Omega` [#Galli2]_. We will use the `WEST `_ +# program to compute the localization factor. This requires creating the input file ``westpp.in`` +# as shown below. # # .. code-block:: text # @@ -123,7 +124,7 @@ # mkdir -p west.westpp.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/box_westpp.json -O west.westpp.save/westpp.json # -# We can now plot the computed localization factor for each of the states: +# We can plot the computed localization factor for each of the states: # # .. code-block:: bash # @@ -151,14 +152,14 @@ # :width: 70% # :target: javascript:void(0) # -# From this plot, it is easy to see that the Kohn-Sham orbitals can be categorized as orbitals -# with low and high localization factors. For the purpose of defining an impurity, we need -# highly localized orbitals, so for this we set a cutoff of 0.06 and choose the orbitals -# that have a localization factor > 0.06. We'll use these orbitals for the calculation of the -# parameters for the effective Hamiltonian in the following section. +# From this plot, it is easy to see that the orbitals can be categorized as orbitals with low and +# high localization factors. For the purpose of defining an impurity, we need highly localized +# orbitals, so we set a cutoff of 0.06 and choose the orbitals that have a localization factor +# :math:`> 0.06`. We'll use these orbitals for the calculation of the parameters needed to construct +# the effective Hamiltonian. # -# Effective Hamiltonian -# ^^^^^^^^^^^^^^^^^^^^^ +# Electronic Integrals +# ^^^^^^^^^^^^^^^^^^^^ # The next step in QDET is to define the effective one-body and two-body integrals for the impurity. # The effective two-body integrals, :math:`v^{eff}` are computed first as matrix elements of the # partially screened static Coulomb potential :math:`W_0^{R}`. @@ -181,17 +182,17 @@ # # t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, # -# In WEST, these parameters for the effective Hamiltonian are calculated by using the ``wfreq.x`` -# executable. The program will: (i) compute the quasiparticle energies, (ii) compute the -# partially screened Coulomb potential, and (iii) finally compute the parameters of the -# effective Hamiltonian. The input file for such a calculation is shown below: +# We use the WEST program to compute these parameters. The program will first compute the +# quasiparticle energies, then computes the partially screened Coulomb potential and finally +# computes the parameters of the effective Hamiltonian. The input file for such a calculations is +# shown below: # # .. code-block:: text # # wstat_control: -# wstat_calculation: S #starts the calculation from scratch -# n_pdep_eigen: 512 #number of PDEP eigenpotentials, set to match the number of electrons -# trev_pdep: 0.00001 #convergence threshold for PDEP eigenvalues +# wstat_calculation: S # starts the calculation from scratch +# n_pdep_eigen: 512 # number of eigenpotentials, set to match the number of electrons +# trev_pdep: 0.00001 # convergence threshold for eigenvalues # # wfreq_control: # wfreq_calculation: XWGQH # compute the quasiparticle corrections and :math:`H^{eff}` parameters @@ -202,7 +203,8 @@ # n_refreq: 300 # number of frequencies on the real axis # ecut_refreq: 2.0 # cutoff for the real frequencies # -# We can execute this calculation as follows: +# We can now execute the calculation with: +# # .. code-block:: bash # # mpirun -n 2 wfreq.x -i wfreq.in > wfreq.out @@ -215,9 +217,12 @@ # mkdir -p west.wfreq.save # wget -N -q https://west-code.org/doc/training/nv_diamond_63/wfreq.json -O west.wfreq.save/wfreq.json # +# This output file contains all the information we need to construct the effective Hamiltonian. +# # Effective Hamiltonian # ^^^^^^^^^^^^^^^^^^^^^ -# We now construct the effective Hamiltonian by importing the electron integral results: +# We now construct the effective Hamiltonian by importing the electron integral results and using +# WEST: # # .. code-block:: python # @@ -225,20 +230,23 @@ # # effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') # -# We can solve for this effective Hamiltonian using a high level method such as the FCI algorithm -# from WESTpy package as: +# The effective Hamiltonian can be solved using a high level method such as the full configuration +# interaction (FCI) algorithm from WEST as: # # .. code-block:: python # # solution = effective_hamiltonian.solve() # -# The solution object is a dictionary containing information about the FCI eigenstates of the -# system, which includes the various excitation energies, spin multiplicities, eigenvectors etc. +# The solution object is a dictionary that contains information about the FCI eigenstates of the +# system, which includes various excitation energies, spin multiplicities, eigenvectors etc. +# More importantly, this effective Hamiltonian can be implemented in a quantum algorithms using +# PennyLane once it is converted to a qubit Hamiltonian. # -# More importantly, this effective Hamiltonian can also be directly used with quantum algorithms in -# PennyLane once it is converted to a qubit Hamiltonian. Since WEST outputs two-electron integrals -# in chemists' notation, a conversion to the physicists' notation is essential for -# compatibility with PennyLane's framework. Here's how to construct the qubit Hamiltonian: +# Quantum Simulation +# ^^^^^^^^^^^^^^^^^^ +# We now map the effective Hamiltonian to the qubit basis. Note that the two-electron obtained +# before are represented in chemists' notation and need to be converted to the physicists' notation +# for compatibility with PennyLane. Here's how to construct the qubit Hamiltonian: # # .. code-block:: python # @@ -253,8 +261,16 @@ # v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) # qubit_op = observable([t, v], mapping="jordan_wigner") # -# We can compare the energies obtained from the diagnolization of this qubit Hamiltonian to the -# solution object above to see that they match. +# We can implement this Hamiltonian in a quantum algorithm such as quantum phase estimation (QPE). +# For simplicity, we just compute the energies obtained from the diagnolization of this qubit +# Hamiltonian: +# +# .. code-block:: python +# +# eigval_qubit = qml.eigvals(qml.SparseHamiltonian(qubit_op.sparse_matrix(), wires = qubit_op.wires)) +# +# You can compare the results and verify that the computed energies match those that we obtained +# before. # # Conclusion # ---------- From 75e80695718180d187d636eaca111128ec4160f4 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 11:34:27 -0400 Subject: [PATCH 59/82] update refs --- demonstrations/tutorial_qdet_embedding.py | 28 ++++++++++++++--------- 1 file changed, 17 insertions(+), 11 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 7aa8070aab..6799270f09 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -290,28 +290,34 @@ # ---------- # # .. [#Galli] -# Joel Davidsson, Mykyta Onizhuk, *et al.*, "Discovery of atomic clock-like spin defects in simple oxides from first principles" -# `ArXiv `__. +# J. Davidsson, M. Onizhuk, C. Vorwerk, G. Galli, +# "Discovery of atomic clock-like spin defects in simple oxides from first principles", +# `arXiv:2302.07523 `__. # # .. [#SJRLee] -# Sebastian J. R. Lee, Feizhi Ding, *et al.*, "Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding." -# `ArXiv `__. +# S. J. R. Lee, F. Ding, F. R. Manby, T. F. Miller III, +# "Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding" +# `arXiv:1903.05830 `__. # # .. [#Gagliardi] -# Abhishek Mitra, Matthew Hermes, *et al.*, "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface." -# `ChemRxiv `__. +# A. Mitra, Matthew Hermes, M. Cho, V. Agarawal, L. Gagliardi, +# "Periodic Density Matrix Embedding for CO Adsorption on the MgO(001)Surface" +# `J. Phys. Chem. Lett. 2022, 13, 7483 `__. # # .. [#Galli2] -# Nan Sheng, Christian Vorwerk, *et al.*, "Green's function formulation of quantum defect embedding theory" +# N. Sheng, C. Vorwerk, M. Govoni, G. Galli, +# "Green's function formulation of quantum defect embedding theory", # `Arxiv `__. # # .. [#Modji] -# Modjtaba S. Zini, Alain Delgado, *et al.*, "Quantum simulation of battery materials using ionic pseudopotentials" -# `ArXiv `__. +# Modjtaba S. Zini, Alain Delgado, *et al.*, +# "Quantum simulation of battery materials using ionic pseudopotentials" +# `arXiv:2203.05493 `__. # # .. [#Baker] -# Jack S. Baker, Pablo A. M. Casares, *et al.*, "Simulating optically-active spin defects with a quantum computer" -# `ArXiv `__. +# Jack S. Baker, Pablo A. M. Casares, *et al.*, +# "Simulating optically-active spin defects with a quantum computer" +# `arXiv:2405.13115 `__. # # About the authors # ----------------- From 8c9ae1263db9b382a26d9c381930ee75e302addb Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 13:03:05 -0400 Subject: [PATCH 60/82] update refs --- demonstrations/tutorial_qdet_embedding.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 6799270f09..910bbea56f 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -307,12 +307,12 @@ # .. [#Galli2] # N. Sheng, C. Vorwerk, M. Govoni, G. Galli, # "Green's function formulation of quantum defect embedding theory", -# `Arxiv `__. +# `arXiv:2203.05493 `__. # # .. [#Modji] -# Modjtaba S. Zini, Alain Delgado, *et al.*, +# M. S. Zini, A. Delgado, *et al.*, # "Quantum simulation of battery materials using ionic pseudopotentials" -# `arXiv:2203.05493 `__. +# `arXiv:2302.07981 `__. # # .. [#Baker] # Jack S. Baker, Pablo A. M. Casares, *et al.*, From d3e42a13d1009df34892bdd01efeaeb9c207cbe5 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 13:13:43 -0400 Subject: [PATCH 61/82] format comments --- demonstrations/tutorial_qdet_embedding.py | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 910bbea56f..81db480148 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -190,18 +190,18 @@ # .. code-block:: text # # wstat_control: -# wstat_calculation: S # starts the calculation from scratch -# n_pdep_eigen: 512 # number of eigenpotentials, set to match the number of electrons -# trev_pdep: 0.00001 # convergence threshold for eigenvalues +# wstat_calculation: S # starts the calculation from scratch +# n_pdep_eigen: 512 # number of eigenpotentials; matches the number of electrons +# trev_pdep: 0.00001 # convergence threshold for eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH # compute the quasiparticle corrections and :math:`H^{eff}` parameters -# macropol_calculation: C # include long-wavelength limit for condensed systems -# l_enable_off_diagonal: true # calculate off-diagonal elements of G_0W_0 self-energy -# n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used +# wfreq_calculation: XWGQH # compute quasiparticle corrections and Hamiltonian parameters +# macropol_calculation: C # include long-wavelength limit for condensed systems +# l_enable_off_diagonal: true # calculate off-diagonal elements of G_0-W_0 self-energy +# n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used # qp_bands: [87,122,123,126,127,128] # impurity orbitals -# n_refreq: 300 # number of frequencies on the real axis -# ecut_refreq: 2.0 # cutoff for the real frequencies +# n_refreq: 300 # number of frequencies on the real axis +# ecut_refreq: 2.0 # cutoff for the real frequencies # # We can now execute the calculation with: # @@ -267,7 +267,8 @@ # # .. code-block:: python # -# eigval_qubit = qml.eigvals(qml.SparseHamiltonian(qubit_op.sparse_matrix(), wires = qubit_op.wires)) +# h_sparse = qml.SparseHamiltonian(qubit_op.sparse_matrix(), wires = qubit_op.wires) +# eigval_qubit = qml.eigvals(h_sparse) # # You can compare the results and verify that the computed energies match those that we obtained # before. From 09330a9e2f906746f789813098e0ca492329ab64 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 15:43:55 -0400 Subject: [PATCH 62/82] update format --- demonstrations/tutorial_qdet_embedding.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 81db480148..8fa622cb8e 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -191,11 +191,11 @@ # # wstat_control: # wstat_calculation: S # starts the calculation from scratch -# n_pdep_eigen: 512 # number of eigenpotentials; matches the number of electrons +# n_pdep_eigen: 512 # number of eigenpotentials; matches number of electrons # trev_pdep: 0.00001 # convergence threshold for eigenvalues # # wfreq_control: -# wfreq_calculation: XWGQH # compute quasiparticle corrections and Hamiltonian parameters +# wfreq_calculation: XWGQH # compute quasiparticle corrections and Hamiltonian params # macropol_calculation: C # include long-wavelength limit for condensed systems # l_enable_off_diagonal: true # calculate off-diagonal elements of G_0-W_0 self-energy # n_pdep_eigen_to_use: 512 # number of PDEP eigenvectors to be used From 4180612d97b54eae9cda0fd560c03e99ad7ca6f8 Mon Sep 17 00:00:00 2001 From: soranjh Date: Fri, 30 May 2025 15:51:52 -0400 Subject: [PATCH 63/82] update equation --- demonstrations/tutorial_qdet_embedding.py | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 8fa622cb8e..458a2ceced 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -87,12 +87,12 @@ # # .. math:: # -# L_n = \int_{V \in \Omega} d^3 r |\Psi_n^{KS}(r)|^2 +# L_n = \int_{V \in \Omega} d^3 r |\Psi_n(r)|^2 # # where :math:`V` is the identified volume including the impurity within the supercell volume -# :math:`\Omega` [#Galli2]_. We will use the `WEST `_ -# program to compute the localization factor. This requires creating the input file ``westpp.in`` -# as shown below. +# :math:`\Omega` and :math:`Psi` is the wavefunction [#Galli2]_. We will use the +# `WEST `_ program to compute the localization factor. +# This requires creating the input file ``westpp.in`` as shown below. # # .. code-block:: text # @@ -154,9 +154,9 @@ # # From this plot, it is easy to see that the orbitals can be categorized as orbitals with low and # high localization factors. For the purpose of defining an impurity, we need highly localized -# orbitals, so we set a cutoff of 0.06 and choose the orbitals that have a localization factor -# :math:`> 0.06`. We'll use these orbitals for the calculation of the parameters needed to construct -# the effective Hamiltonian. +# orbitals, so we set a cutoff of :math:`0.06` and choose the orbitals that have a localization +# factor larger than :math:`0.06`. We'll use these orbitals for the calculation of the parameters +# needed to construct the effective Hamiltonian. # # Electronic Integrals # ^^^^^^^^^^^^^^^^^^^^ From 463f8628fca04c06cefd57679266ecd27ff31718 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Tue, 3 Jun 2025 21:16:38 -0400 Subject: [PATCH 64/82] Update demonstrations/tutorial_qdet_embedding.py --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 458a2ceced..4a59b62f7d 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -90,7 +90,7 @@ # L_n = \int_{V \in \Omega} d^3 r |\Psi_n(r)|^2 # # where :math:`V` is the identified volume including the impurity within the supercell volume -# :math:`\Omega` and :math:`Psi` is the wavefunction [#Galli2]_. We will use the +# :math:`\Omega` and :math:`\Psi` is the wavefunction [#Galli2]_. We will use the # `WEST `_ program to compute the localization factor. # This requires creating the input file ``westpp.in`` as shown below. # From a021fcd9b650d2967e53fcccaa5e6c79c29a7c74 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:26:03 -0400 Subject: [PATCH 65/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 11 ++++------- 1 file changed, 4 insertions(+), 7 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 4a59b62f7d..b9a6f47e1c 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -1,13 +1,10 @@ r"""Quantum Defect Embedding Theory (QDET) ========================================= -Efficient simulation of the electronic structure of materials and molecules remains a -significant challenge due to the prohibitive costs of available classical methods. However, many -interesting problems in quantum chemistry and condensed matter physics feature a strongly correlated -region, which requires accurate quantum treatment, embedded within a larger environment that could -be properly treated with cheaper approximations. Example of such systems include point defects in +Many interesting problems in quantum chemistry and materials science feature a strongly correlated +region embedded within a larger environment. Example of such systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_ and surface phenomenon such as adsorption -[#Gagliardi]_. Such systems can be accurately simulated with embedding theories which effectively -capture the strong electronic correlations in the active region with high accuracy while accounting +[#Gagliardi]_. Such systems can be accurately simulated with **embedding theories**, which effectively +capture the strong electronic correlations in the active region with high accuracy, while accounting for the environment in a more approximate manner. In this demo, we show how to implement quantum defect embedding theory (QDET) [#Galli]_. This method From e0c74642ec2b2a9f739f0956e9bdf597bdfa767a Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:26:53 -0400 Subject: [PATCH 66/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index b9a6f47e1c..a7e3a7340f 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -8,9 +8,8 @@ for the environment in a more approximate manner. In this demo, we show how to implement quantum defect embedding theory (QDET) [#Galli]_. This method -has been successfully applied to study systems such as defects in CaO [#Galli]_ and to calculate -excitations of the negatively charged nitrogen-vacancy defect in diamond [#Galli2]_. QDET can be implemented for -calculating both ground and excited states as well as dynamic properties of materials. These make +has been successfully applied to study systems such as defects in calcium oxide [#Galli]_ and to calculate +excitations of the negatively charged nitrogen-vacancy defect in diamond [#Galli2]_. QDET can be used to calculate ground states, excited states, and dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation of materials. Another important advantage of QDET is the compatibility of the method with quantum algorithms as we explain in the following sections. From 5adff536696107fc4504e2c0728c1a4e0ea52ad9 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:27:16 -0400 Subject: [PATCH 67/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a7e3a7340f..a716590f98 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -32,9 +32,9 @@ # H^{eff} = \sum_{ij} t_{ij}^{eff}a_i^{\dagger}a_j + \frac{1}{2}\sum_{ijkl} v_{ijkl}^{eff}a_i^{\dagger}a_{j}^{\dagger}a_ka_l, # # where :math:`t_{ij}^{eff}` and :math:`v_{ijkl}^{eff}` represent the effective one-body and -# two-body integrals, respectively, and :math:`ijkl` span over the orbitals inside the impurity. -# This Hamiltonian describes a simplified representation of the complex quantum system that is -# computationally tractable while it properly captures the essential physics of the problem. +# two-body integrals, respectively, and the indices :math:`ijkl` span over the orbitals inside the impurity. +# This Hamiltonian describes a simplified representation of the quantum system that is more +# computationally tractable, while properly capturing the essential physics of the problem. # # Implementation # -------------- From 1f7988b21c338561f43188dad435f640c0eef7e3 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:27:24 -0400 Subject: [PATCH 68/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index a716590f98..dea3ec38e8 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -40,7 +40,7 @@ # -------------- # A QDET simulation typically starts by obtaining a meanfield approximation of the whole system # using efficient quantum chemistry methods such as density functional theory (DFT). These -# calculations provide a set of orbitals that are partitioned into impurity and bath orbitals. +# calculations provide a set of orbitals that are partitioned into **impurity** and **bath** orbitals. # The effective Hamiltonian is constructed from the impurity orbitals and is subsequently solved # by using either a high accuracy classical method or a quantum algorithm. Let's implement these # steps for an example! From 7d591cf5c12231445b5c0f5a21daa2b0c2d2b603 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:27:43 -0400 Subject: [PATCH 69/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index dea3ec38e8..d8862d458a 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -59,7 +59,7 @@ # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf # wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf # -# Next, we need to create the input file for running QUANTUM ESPRESSO. The input file contains +# Next, we need to create the input file for running QUANTUM ESPRESSO. This contains # information about the system and the DFT calculations. More details on how to construct the input # file can be found in QUANTUM ESPRESSO `documentation `_ # page. For the system taken here, the input file can be downloaded with From 7ec48c7b65e177c03b3092870e1d76db131c53d2 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:27:59 -0400 Subject: [PATCH 70/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index d8862d458a..f1a6178719 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -178,9 +178,9 @@ # # t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, # -# We use the WEST program to compute these parameters. The program will first compute the -# quasiparticle energies, then computes the partially screened Coulomb potential and finally -# computes the parameters of the effective Hamiltonian. The input file for such a calculations is +# We use the WEST program to compute these parameters. WEST will first compute the +# quasiparticle energies, then the partially screened Coulomb potential, and finally +# the parameters of the effective Hamiltonian. The input file for such a calculations is # shown below: # # .. code-block:: text From ecf5a81ef88c58b70372a70ea06c4eb85a5e9633 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:28:26 -0400 Subject: [PATCH 71/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index f1a6178719..7eda160198 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -83,7 +83,7 @@ # # .. math:: # -# L_n = \int_{V \in \Omega} d^3 r |\Psi_n(r)|^2 +# L_n = \int_{V \in \Omega} d^3 r |\Psi_n(r)|^2, # # where :math:`V` is the identified volume including the impurity within the supercell volume # :math:`\Omega` and :math:`\Psi` is the wavefunction [#Galli2]_. We will use the From 412c9ce614ab09b828f5b8321d4886114f1de0b2 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:29:13 -0400 Subject: [PATCH 72/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 7eda160198..49443dd583 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -112,8 +112,8 @@ # mpirun -n 2 westpp.x -i westpp.in > westpp.out # # This creates the file ``westpp.json`` which contains the information we need here. Since -# computational resources required to run the calculation are large, we just download a pre-computed -# file with: +# computational resources required to run the calculation are large, for the purpose of this tutorial we just +# download a pre-computed file with: # # .. code-block:: bash # From 1d256d01fb750bc88d2286df68f6536093af0b72 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:29:34 -0400 Subject: [PATCH 73/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 49443dd583..33a1e96899 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -150,7 +150,7 @@ # # From this plot, it is easy to see that the orbitals can be categorized as orbitals with low and # high localization factors. For the purpose of defining an impurity, we need highly localized -# orbitals, so we set a cutoff of :math:`0.06` and choose the orbitals that have a localization +# orbitals, so we set a cutoff of :math:`0.06` , illustrated by the red dashed line, and choose the orbitals that have a localization # factor larger than :math:`0.06`. We'll use these orbitals for the calculation of the parameters # needed to construct the effective Hamiltonian. # From 3ff97ad8108f3ec39aed578091ad9c0e91a7d632 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:29:54 -0400 Subject: [PATCH 74/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 33a1e96899..49cd8cc873 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -157,7 +157,7 @@ # Electronic Integrals # ^^^^^^^^^^^^^^^^^^^^ # The next step in QDET is to define the effective one-body and two-body integrals for the impurity. -# The effective two-body integrals, :math:`v^{eff}` are computed first as matrix elements of the +# The effective two-body integrals :math:`v^{eff}` are computed first as matrix elements of the # partially screened static Coulomb potential :math:`W_0^{R}`. # # .. math:: From 5771176a328eb110043683dacc611ab0e060c103 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:30:12 -0400 Subject: [PATCH 75/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 49cd8cc873..72cc4b9912 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -164,7 +164,7 @@ # # v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, # -# where :math:`W_0^R` results from screening the bare Coulomb potential, :math:`v`, with the reduced +# where :math:`W_0^R` results from screening the bare Coulomb potential :math:`v` with the reduced # polarizability, :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and # :math:`P_{imp}` is the impurity's polarizability. Since solving the effective Hamiltonian # accounts for the exchange and correlation interactions between the active electrons, we remove From da663bad20551cd1f186dee7538ee09d468aadc4 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:30:32 -0400 Subject: [PATCH 76/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 72cc4b9912..82c96caf54 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -165,10 +165,10 @@ # v_{ijkl}^{eff} = [W_0^{R}]_{ijkl}, # # where :math:`W_0^R` results from screening the bare Coulomb potential :math:`v` with the reduced -# polarizability, :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and +# polarizability :math:`P_0^R = P - P_{imp}`, where :math:`P` is the system's polarizability and # :math:`P_{imp}` is the impurity's polarizability. Since solving the effective Hamiltonian # accounts for the exchange and correlation interactions between the active electrons, we remove -# these interactions from the Kohn-Sham Hamiltonian, :math:`H^{KS}`, to avoid double counting them. +# these interactions from the Kohn-Sham Hamiltonian :math:`H^{KS}` to avoid double counting them. # # The one-body term :math:`t^{eff}` is obtained by subtracting from the Kohn-Sham Hamiltonian the # double-counting term accounting for electrostatic and exchange-correlation interactions in the From 3770219966eedad478290afff91008714c716274 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Date: Mon, 16 Jun 2025 20:30:53 -0400 Subject: [PATCH 77/82] Update demonstrations/tutorial_qdet_embedding.py Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 82c96caf54..f95b967e2d 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -176,7 +176,7 @@ # # .. math:: # -# t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}, +# t_{ij}^{eff} = H_{ij}^{KS} - t_{ij}^{dc}. # # We use the WEST program to compute these parameters. WEST will first compute the # quasiparticle energies, then the partially screened Coulomb potential, and finally From c2912335776143de2223147a953c38242b217bce Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Mon, 16 Jun 2025 21:25:39 -0400 Subject: [PATCH 78/82] Addressed comments --- demonstrations/tutorial_qdet_embedding.py | 49 +++++++++++++---------- 1 file changed, 28 insertions(+), 21 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index f95b967e2d..d43b959bbe 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -52,7 +52,8 @@ # The DFT calculations are performed with the `QUANTUM ESPRESSO `_ # package. This requires downloading pseudopotentials [#Modji]_ for each atomic species # in the system from the QUANTUM ESPRESSO `database `_. -# We have carbon and nitrogen in our system and download their pseudopotentials with +# To prepare our system, the necessary carbon and nitrogen pseudopotentials can be downloaded by executing +# the following commands through the terminal or command prompt: # # .. code-block:: bash # @@ -68,8 +69,8 @@ # # wget -N -q https://west-code.org/doc/training/nv_diamond_63/pw.in # -# We can now perform the DFT calculations by running ``pw.x`` on the input file ``pw.in`` and save -# the results in ``pw.out``. +# DFT calculations can now be initiated using the `pw.x` executable in `WEST`, taking `pw.in` as the input file +# and directing the output to `pw.out`. This process is parallelized across 2 cores using mpirun. # # .. code-block:: bash # @@ -88,7 +89,9 @@ # where :math:`V` is the identified volume including the impurity within the supercell volume # :math:`\Omega` and :math:`\Psi` is the wavefunction [#Galli2]_. We will use the # `WEST `_ program to compute the localization factor. -# This requires creating the input file ``westpp.in`` as shown below. +# This requires the westpp.in input file, example for which is shown below. Here, we specify the +# box parameters within which the localization factor is being computed; the vectors for this box are provided in +# in atomic units as [x_start, x_end, y_start, y_end, z_start, z_end]. # # .. code-block:: text # @@ -105,14 +108,15 @@ # - 6.28 # - 10.28 # -# We can now perform the calculation with +# The calculation can now be performed by running the westpp.x executable from WEST using mpirun to +# parallelize it across two cores. # # .. code-block:: bash # # mpirun -n 2 westpp.x -i westpp.in > westpp.out # # This creates the file ``westpp.json`` which contains the information we need here. Since -# computational resources required to run the calculation are large, for the purpose of this tutorial we just +# computational resources required to run the calculation are large, for the purpose of this tutorial we just # download a pre-computed file with: # # .. code-block:: bash @@ -137,7 +141,7 @@ # plt.plot(x,y,'o') # plt.axhline(y=0.08,linestyle='--',color='red') # -# plt.xlabel('KS index') +# plt.xlabel('Kohn-Sham orbital index') # plt.ylabel('Localization factor') # # plt.show() @@ -235,8 +239,10 @@ # # The solution object is a dictionary that contains information about the FCI eigenstates of the # system, which includes various excitation energies, spin multiplicities, eigenvectors etc. -# More importantly, this effective Hamiltonian can be implemented in a quantum algorithms using -# PennyLane once it is converted to a qubit Hamiltonian. +# More importantly, while FCI handles small embedded effective Hamiltonians with ease, it quickly +# hits a wall with larger impurities. This is precisely where quantum computing steps in, offering +# the scalability needed to tackle such complex systems. The first step to solving these effective +# Hamiltonians via quantum algorithms in PennyLane, is to convert them to qubit Hamiltonians. # # Quantum Simulation # ^^^^^^^^^^^^^^^^^^ @@ -246,16 +252,17 @@ # # .. code-block:: python # -# from pennylane.qchem import one_particle, two_particle, observable -# import numpy as np -# -# effective_hamiltonian = QDETResult(filename='west.wfreq.save/wfreq.json') -# -# one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri -# -# t = one_particle(one_e[0]) -# v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -# qubit_op = observable([t, v], mapping="jordan_wigner") +from pennylane.qchem import one_particle, two_particle, observable +import numpy as np + +effective_hamiltonian = QDETResult(filename="west.wfreq.save/wfreq.json") + +one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri + +t = one_particle(one_e[0]) +v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) +qubit_op = observable([t, v], mapping="jordan_wigner") +print(qubit_op) # # We can implement this Hamiltonian in a quantum algorithm such as quantum phase estimation (QPE). # For simplicity, we just compute the energies obtained from the diagnolization of this qubit @@ -274,8 +281,8 @@ # Quantum defect embedding theory is a novel framework for simulating strongly correlated # quantum systems and has been successfully used for studying defects in solids. Applicability of # QDET however is not limited to defects, it can be used for other systems where a strongly -# correlated subsystem is embedded in a weakly correlated environment. Additionally, QDET is able to -# correct the interaction double counting issue within the active space faced by a variety of +# correlated subsystem is embedded in a weakly correlated environment. Additionally, QDET is able to +# correct the interaction double counting issue within the active space faced by a variety of # other embedding theories. The Green's function based formulation of QDET ensures # exact removal of double counting corrections at GW level of theory, thus removing the # approximation present in the initial DFT based formulation. 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zq(KhIz0nXt7%*4~LYXJ?e}?XbyMMtpxRr%D1h6@URZDMLPQ(czfAE5y3hcj+$$-6L z@&B27gdsZr@0Som?Ef1D!vx*^e^xqZf&b6wgNm~JzcCt7M#%qJtl(z&|1*N&(I)?I mOaZj6{%4u||9Gi^f8blYLFuCQgkt|)TTV(zvPRq_^#1{dW=8D* diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index d43b959bbe..7381f4c865 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -9,8 +9,9 @@ In this demo, we show how to implement quantum defect embedding theory (QDET) [#Galli]_. This method has been successfully applied to study systems such as defects in calcium oxide [#Galli]_ and to calculate -excitations of the negatively charged nitrogen-vacancy defect in diamond [#Galli2]_. QDET can be used to calculate ground states, excited states, and dynamic properties of materials. These make -QDET a powerful method for affordable quantum simulation of materials. Another important advantage +excitations of the negatively charged nitrogen-vacancy defect in diamond [#Galli2]_. QDET can be used to calculate ground states, +excited states, and dynamic properties of materials. These make QDET a powerful method for affordable quantum simulation +of materials. Another important advantage of QDET is the compatibility of the method with quantum algorithms as we explain in the following sections. @@ -237,6 +238,30 @@ # # solution = effective_hamiltonian.solve() # +# Using :code:`solve()` prints the excitation energies, spin multiplicity and relative occupation of +# the active orbitals. +# +# .. code-block:: python +# +# ====================================================================== +# Building effective Hamiltonian... +# nspin: 1 +# occupations: [[2. 2. 2. 2. 1. 1.]] +# ===================================================================== +# diag[1RDM - 1RDM(GS)] +# E [eV] char 87 122 123 126 127 128 +# 0 0.000 3- 0.000 0.000 0.000 0.000 0.000 0.000 +# 1 0.436 1- -0.001 -0.009 -0.018 -0.067 0.004 0.091 +# 2 0.436 1- -0.001 -0.009 -0.018 -0.067 0.092 0.002 +# 3 1.251 1- -0.002 -0.019 -0.023 -0.067 0.054 0.057 +# 4 1.939 3- -0.003 -0.010 -0.127 -0.860 1.000 0.000 +# 5 1.940 3- -0.003 -0.010 -0.127 -0.860 0.000 1.000 +# 6 2.935 1- -0.000 -0.032 -0.043 -0.855 0.929 0.002 +# 7 2.936 1- -0.000 -0.032 -0.043 -0.855 0.002 0.929 +# 8 4.661 1- -0.006 -0.054 -0.188 -1.672 0.960 0.960 +# 9 5.080 3- -0.014 -0.698 -0.213 -0.075 1.000 0.000 +# ---------------------------------------------------------------------- +# # The solution object is a dictionary that contains information about the FCI eigenstates of the # system, which includes various excitation energies, spin multiplicities, eigenvectors etc. # More importantly, while FCI handles small embedded effective Hamiltonians with ease, it quickly @@ -252,29 +277,20 @@ # # .. code-block:: python # -from pennylane.qchem import one_particle, two_particle, observable -import numpy as np - -effective_hamiltonian = QDETResult(filename="west.wfreq.save/wfreq.json") - -one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri - -t = one_particle(one_e[0]) -v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) -qubit_op = observable([t, v], mapping="jordan_wigner") -print(qubit_op) +# from pennylane.qchem import one_particle, two_particle, observable +# import numpy as np # -# We can implement this Hamiltonian in a quantum algorithm such as quantum phase estimation (QPE). -# For simplicity, we just compute the energies obtained from the diagnolization of this qubit -# Hamiltonian: +# effective_hamiltonian = QDETResult(filename="west.wfreq.save/wfreq.json") # -# .. code-block:: python +# one_e, two_e = effective_hamiltonian.h1e, effective_hamiltonian.eri # -# h_sparse = qml.SparseHamiltonian(qubit_op.sparse_matrix(), wires = qubit_op.wires) -# eigval_qubit = qml.eigvals(h_sparse) +# t = one_particle(one_e[0]) +# v = two_particle(np.swapaxes(two_e[0][0], 1, 3)) +# qubit_op = observable([t, v], mapping="jordan_wigner") # -# You can compare the results and verify that the computed energies match those that we obtained -# before. +# We can use this Hamiltonian in a quantum algorithm such as quantum phase estimation (QPE). +# As an exercise, you can compare the results 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2 deletions(-) diff --git a/demonstrations/tutorial_qdet_embedding.metadata.json b/demonstrations/tutorial_qdet_embedding.metadata.json index 5f4f20f987..c3eaf9c903 100644 --- a/demonstrations/tutorial_qdet_embedding.metadata.json +++ b/demonstrations/tutorial_qdet_embedding.metadata.json @@ -15,11 +15,11 @@ "previewImages": [ { "type": "thumbnail", - "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_qdet_hamiltonians.png" + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_how_to_build_qdet_hamiltonian.png" }, { "type": "large_thumbnail", - "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_qdet_hamiltonians.png" + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_how_to_build_qdet_hamiltonian.png" } ], "seoDescription": "Learn how to build a Quantum Defect Embedding Theory (QDET) Hamiltonian.", From 071bb0ea01b40a4a624f190f006007e47e5cf880 Mon Sep 17 00:00:00 2001 From: Diksha Dhawan Date: Mon, 30 Jun 2025 13:47:03 -0400 Subject: [PATCH 82/82] fixed rendering --- demonstrations/tutorial_qdet_embedding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qdet_embedding.py b/demonstrations/tutorial_qdet_embedding.py index 3966d25fa7..1d19f03def 100644 --- a/demonstrations/tutorial_qdet_embedding.py +++ b/demonstrations/tutorial_qdet_embedding.py @@ -241,7 +241,7 @@ # Using :code:`solve()` prints the excitation energies, spin multiplicity and relative occupation of # the active orbitals. # -# .. code-block:: python +# .. code-block:: text # # ====================================================================== # Building effective Hamiltonian...

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