From 7db83abcfeb4b31ff8d2ac78572f30b95dc4fe0a Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Wed, 8 May 2024 15:58:29 -0400 Subject: [PATCH 01/31] add initial draft for qcbm demo --- demonstrations/tutorial_qcbm.py | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) create mode 100644 demonstrations/tutorial_qcbm.py diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py new file mode 100644 index 0000000000..58dd7db7a8 --- /dev/null +++ b/demonstrations/tutorial_qcbm.py @@ -0,0 +1,18 @@ +""" +.. qcbm: + +QCBM with tensor networks ansatz +=============== + +.. meta:: + :property="og:description": Implementing the Quantum Circuit Born Machine (QCBM) using a tensor network ansatz + :property="og:image": https://pennylane.ai/qml/_static/demonstration_assets//qaoa_maxcut_partition.png + +.. related:: + tutorial_qaoa_intro Intro to QAOA + +*Author: Ahmed Darwish and Emiliano Godinez — Posted: 08 May 2024. Last updated: 08 May 2024.* + +""" + +############################################################################## From ebae9bdf03fc96cb4528db371e68b55c003073b7 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Thu, 9 May 2024 13:59:50 -0400 Subject: [PATCH 02/31] add structure to tutorial qcbm --- demonstrations/tutorial_qcbm.py | 50 ++++++++++++++++++++++++++++++++- 1 file changed, 49 insertions(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 58dd7db7a8..0750a7e14a 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -9,10 +9,58 @@ :property="og:image": https://pennylane.ai/qml/_static/demonstration_assets//qaoa_maxcut_partition.png .. related:: - tutorial_qaoa_intro Intro to QAOA *Author: Ahmed Darwish and Emiliano Godinez — Posted: 08 May 2024. Last updated: 08 May 2024.* +In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by `Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) `__. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. """ ############################################################################## +# Generative modeling and quantum physics +# ----------------------- +# In the classical setup of unsupervised learning, a generative statistical model is tasked with creating new data instances that follow the probability distribution of the input training data. This is in contrast to other statistical models like the discriminative model, which allows us to "tell apart" the different instances present in the the input data, assigning a label to each of them. +# +# add image here showing an example of "generative model" +# +# An important trait of the generative model that allows for this generation of new samples is rooted on its ability to capture correlations present in the input data. Among the different models employed in the literature for generative machine learning, the so called "Born machine" model is based on representing the probability distribution :math`p(x)` in terms of the amplitudes of the quantum wave function :math`\ket{\psi}`, with the relation given by Born's rule +# +# .. math:: +# p(x) = \norm*{\bra{x}\ket{\psi}}^2 +# +# As done in https://arxiv.org/pdf/1901.02217, the efficient representation provided by tensor network ansätze invites us to represent the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the training data, this making them suitable candidates be employed in the generative model. +# +# add tensor network image with psi as label both for MPS and TTN. +# +# Tensor networks and Quantum Circuits +# ----------------------- +# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wave function in order to approximate the target probability distribution. While many algorithms have been proposed to sample tensor networks classes efficiently (https://arxiv.org/pdf/1201.3974, https://arxiv.org/pdf/2401.10330), as suggested in https://arxiv.org/pdf/1809.07442, this task appears as a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. As presented in https://arxiv.org/pdf/1801.07686, this approach employing quantum circuits to model the probabililty distribution is known as the Quantum Circuit Born Machine (QCBM). +# +# The problem formulation starts by looking at the training data set :math:`\mathcal{D} = (\mathrb{x}^{(1)}, \mathrb{x}^{(2)}, ldots, \mathrb{x}^{(D)})` made up of :math`D` binary vectors of length :math`N`. Each of this vectors have an associated probability of occurring within the data, resulting in the target probability distribution :math`P_{\mathcal{D}}`. For a quantum circuit with :math`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational states and the input vectors +# +# .. math:: +# \mathrb{x} := (x_1, x_2, \ldots, x_N) \leftrightarrow \ket{\mathrb{x}} := \ket{x_1, x_2, \ldots, x_N} +# +# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math`\theta`, such that the output state vector is defined as :math`\ket{\psi(\theta)} = U(\theta) \ket{0}`. +# +# add drawing of circuit. +# +# This in turn results in the probability of finding the output wave function in the computational :math:`\ket{\mathrb{x}}` expressed as +# +# .. math:: +# P_\theta(\mathrb{x}) = \norm*{ \bra{\mathrb{x}}\ket{\psi(\theta)}}^2 +# +# We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter vector :math`\theta` in order to obtain the wave function that best approximates the target distribution. In other words, we can express this problem as the minimization problem +# +# .. math:: +# min_{\theta} C(P_\theta(\mathrb{x})) +# +# where :math`C` is the cost funciton +# In this tutorial we follow the hybrid algorithm introduced in +# +# Tensor Network Ansatz +# --------------------------- +# +# Pennylane implementation +# --------------------------- + +I can then explain what are generative models generally, how born machine is one model possible, and how this has been attempted by using tensor networks. On the other hand it has also been attempted with quantum circuits, and here we combine both methods. I can say "quantum circuits are a particular instance of tensor networks, and therefore there is a natural connection" (cite the diagrammatic representation) From 40bc4bf451c40e75ced96c116b853776c3241d63 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Thu, 9 May 2024 16:38:06 -0400 Subject: [PATCH 03/31] add ansatz and qc sections in qcbm tutorial --- demonstrations/tutorial_qcbm.py | 71 ++++++++++++++++++++++++++++----- 1 file changed, 60 insertions(+), 11 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 0750a7e14a..49a453051e 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -12,7 +12,7 @@ *Author: Ahmed Darwish and Emiliano Godinez — Posted: 08 May 2024. Last updated: 08 May 2024.* -In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by `Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) `__. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. +In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by `Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. """ ############################################################################## @@ -22,45 +22,94 @@ # # add image here showing an example of "generative model" # -# An important trait of the generative model that allows for this generation of new samples is rooted on its ability to capture correlations present in the input data. Among the different models employed in the literature for generative machine learning, the so called "Born machine" model is based on representing the probability distribution :math`p(x)` in terms of the amplitudes of the quantum wave function :math`\ket{\psi}`, with the relation given by Born's rule +# An important trait of the generative model that allows for this generation of new samples is rooted on its ability to capture correlations present in the input data. Among the different models employed in the literature for generative machine learning, the so called "Born machine" model is based on representing the probability distribution :math:`p(x)` in terms of the amplitudes of the quantum wave function :math:`\ket{\psi}`, with the relation given by Born's rule # # .. math:: # p(x) = \norm*{\bra{x}\ket{\psi}}^2 # -# As done in https://arxiv.org/pdf/1901.02217, the efficient representation provided by tensor network ansätze invites us to represent the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the training data, this making them suitable candidates be employed in the generative model. +# As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the training data, this making them suitable candidates be employed in the generative model. # # add tensor network image with psi as label both for MPS and TTN. # # Tensor networks and Quantum Circuits # ----------------------- -# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wave function in order to approximate the target probability distribution. While many algorithms have been proposed to sample tensor networks classes efficiently (https://arxiv.org/pdf/1201.3974, https://arxiv.org/pdf/2401.10330), as suggested in https://arxiv.org/pdf/1809.07442, this task appears as a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. As presented in https://arxiv.org/pdf/1801.07686, this approach employing quantum circuits to model the probabililty distribution is known as the Quantum Circuit Born Machine (QCBM). +# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wave function in order to approximate the target probability distribution. While many algorithms have been proposed to sample tensor networks classes efficiently ([#Ferris]_, [#Ballarin]_), as suggested in [#Harrow]_, this task appears as a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. As presented in [#Benedetti]_, this approach employing quantum circuits to model the probabililty distribution is known as the Quantum Circuit Born Machine (QCBM). # -# The problem formulation starts by looking at the training data set :math:`\mathcal{D} = (\mathrb{x}^{(1)}, \mathrb{x}^{(2)}, ldots, \mathrb{x}^{(D)})` made up of :math`D` binary vectors of length :math`N`. Each of this vectors have an associated probability of occurring within the data, resulting in the target probability distribution :math`P_{\mathcal{D}}`. For a quantum circuit with :math`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational states and the input vectors +# The problem formulation starts by looking at the training data set :math:`\mathcal{D} = (\mathrb{x}^{(1)}, \mathrb{x}^{(2)}, ldots, \mathrb{x}^{(D)})` made up of :math:`D` binary vectors of length :math:`N`. Each of this vectors have an associated probability of occurring within the data, resulting in the target probability distribution :math:`P_{\mathcal{D}}`. For a quantum circuit with :math:`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational states and the input vectors # # .. math:: # \mathrb{x} := (x_1, x_2, \ldots, x_N) \leftrightarrow \ket{\mathrb{x}} := \ket{x_1, x_2, \ldots, x_N} # -# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math`\theta`, such that the output state vector is defined as :math`\ket{\psi(\theta)} = U(\theta) \ket{0}`. +# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. # # add drawing of circuit. # -# This in turn results in the probability of finding the output wave function in the computational :math:`\ket{\mathrb{x}}` expressed as +# Then, we can look at the probability of finding the output wave function in the computational basis state :math:`\ket{\mathrb{x}}` expressed as # # .. math:: # P_\theta(\mathrb{x}) = \norm*{ \bra{\mathrb{x}}\ket{\psi(\theta)}}^2 # -# We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter vector :math`\theta` in order to obtain the wave function that best approximates the target distribution. In other words, we can express this problem as the minimization problem +# We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter vector :math:`\theta` in order to obtain the wave function that best approximates the target distribution. In other words, we can formulate this problem as the minimization # # .. math:: -# min_{\theta} C(P_\theta(\mathrb{x})) +# min_{\theta} C(P_\theta(\mathrb{x})), +# +# where :math:`C` is the cost function to be optimized, which can take different forms based on the specific scenario, with the common denominator being that all of them should quantify the difference between the target probability and the probability distribution obtained from the quantum circuit. Due to the nature of the finite sampling used to estimate the distribution, analogous to what is done in classsical generative machine learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. +# +# :math:: +# C(\theta) = \sum_\mathrb{x} P_D(\mathrb{x}) ln \left ( \frac{P_D(\mathrb{x})}{P_\theta(\mathrb{x})} \right) # -# where :math`C` is the cost funciton -# In this tutorial we follow the hybrid algorithm introduced in # # Tensor Network Ansatz # --------------------------- +# The algorithm presented in [#Benedetti]_, proposes the use of a hardware-efficient ansatz to prepare the probability distriubtion using a quantum circuit. However, in this work we take inspiration from previous approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. In particular, we take into consideration the local correlations of the data, and employ the MPS and TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ for a deeper study of these ansätze. +# # # Pennylane implementation # --------------------------- +# +# References +# ^^^^^^^^^^ +# +# .. [#Benedetti] +# M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, +# *npj Quantum Information* **5**, 1 (2019), ISSN 2056-6387, +# URL ``__ +# +# .. [#Cheng] +# S. Cheng, L. Wang, T. Xiang, and P. Zhang, +# *Physical Review B* **99**, 15 (2019), ISSN 2469-9969, +# URL ``__ + +# .. [#Ferris] +# A. J. Ferris and G. Vidal, +# *Physical Review B* **85**, 16 (2012), ISSN 1550-235X, +# URL ``__ + +# .. [#Ballarin] +# M. Ballarin, P. Silvi, S. Montangero, and D. Jaschke, +# "Optimal sampling of tensor networks targeting wave function's fast decaying tails," (2024), +# arXiv:2401.10330 [quant-ph], +# URL ``__ + +# .. [#Harrow] +# A. W. Harrow and A. Montanaro, +# *Nature* **549**, 7671, 203–209 (2017), ISSN 1476-4687, +# URL ``__ + +# .. [#Goodfellow] +# I. Goodfellow, Y. Bengio, and A. Courville, +# *Deep Learning* (2016), +# MIT Press, +# URL ``__ + +# .. [#Han] +# Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang, +# *Physical Review X* **8**, 3 (2018), ISSN 2160-3308, +# URL ``__ + + + + I can then explain what are generative models generally, how born machine is one model possible, and how this has been attempted by using tensor networks. On the other hand it has also been attempted with quantum circuits, and here we combine both methods. I can say "quantum circuits are a particular instance of tensor networks, and therefore there is a natural connection" (cite the diagrammatic representation) From d9eddc1ac91c8b1251b56b3deaeb183e7f5e9b19 Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Thu, 9 May 2024 17:26:55 -0400 Subject: [PATCH 04/31] Added code to the demo --- demonstrations/tutorial_qcbm.py | 268 ++++++++++++++++++++++++++++---- 1 file changed, 236 insertions(+), 32 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 49a453051e..3ee1b96c24 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -18,56 +18,259 @@ ############################################################################## # Generative modeling and quantum physics # ----------------------- -# In the classical setup of unsupervised learning, a generative statistical model is tasked with creating new data instances that follow the probability distribution of the input training data. This is in contrast to other statistical models like the discriminative model, which allows us to "tell apart" the different instances present in the the input data, assigning a label to each of them. -# +# In the classical setup of unsupervised learning, a generative statistical model is tasked with creating +# new data instances that follow the probability distribution of the input training data. This is in contrast +# to other statistical models like the discriminative model, which allows us to "tell apart" the different instances +# present in the the input data, assigning a label to each of them. +# # add image here showing an example of "generative model" # -# An important trait of the generative model that allows for this generation of new samples is rooted on its ability to capture correlations present in the input data. Among the different models employed in the literature for generative machine learning, the so called "Born machine" model is based on representing the probability distribution :math:`p(x)` in terms of the amplitudes of the quantum wave function :math:`\ket{\psi}`, with the relation given by Born's rule -# +# An important trait of the generative model that allows for this generation of new samples is rooted on its +# ability to capture correlations present in the input data. Among the different models employed in the literature +# for generative machine learning, the so called "Born machine" model is based on representing the probability +# distribution :math:`p(x)` in terms of the amplitudes of the quantum wave function :math:`\ket{\psi}`, with the +# relation given by Born's rule +# # .. math:: # p(x) = \norm*{\bra{x}\ket{\psi}}^2 # -# As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the training data, this making them suitable candidates be employed in the generative model. -# +# As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent +# the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product +# States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the +# training data, this making them suitable candidates be employed in the generative model. +# # add tensor network image with psi as label both for MPS and TTN. -# +# # Tensor networks and Quantum Circuits # ----------------------- -# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wave function in order to approximate the target probability distribution. While many algorithms have been proposed to sample tensor networks classes efficiently ([#Ferris]_, [#Ballarin]_), as suggested in [#Harrow]_, this task appears as a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. As presented in [#Benedetti]_, this approach employing quantum circuits to model the probabililty distribution is known as the Quantum Circuit Born Machine (QCBM). -# -# The problem formulation starts by looking at the training data set :math:`\mathcal{D} = (\mathrb{x}^{(1)}, \mathrb{x}^{(2)}, ldots, \mathrb{x}^{(D)})` made up of :math:`D` binary vectors of length :math:`N`. Each of this vectors have an associated probability of occurring within the data, resulting in the target probability distribution :math:`P_{\mathcal{D}}`. For a quantum circuit with :math:`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational states and the input vectors -# +# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wavefunction +# in order to approximate the target probability distribution. While many algorithms have been proposed to sample +# tensor networks classes efficiently ([#Ferris]_, [#Ballarin]_), as suggested in [#Harrow]_, this task appears as +# a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. +# As presented in [#Benedetti]_, this approach employing quantum circuits to model the probabililty distribution is +# known as the Quantum Circuit Born Machine (QCBM). +# +# The problem formulation starts by looking at the training dataset +# :math:`\mathcal{D} = (\mathrb{x}^{(1)}, \mathrb{x}^{(2)}, ldots, \mathrb{x}^{(D)})` made up of :math:`D` binary +# vectors of length :math:`N`. Each of this vectors have an associated probability of occurring within the data, +# resulting in the target probability distribution :math:`P_{\mathcal{D}}`. For a quantum circuit +# with :math:`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational +# states and the input vectors +# # .. math:: # \mathrb{x} := (x_1, x_2, \ldots, x_N) \leftrightarrow \ket{\mathrb{x}} := \ket{x_1, x_2, \ldots, x_N} -# -# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. -# +# +# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a +# vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. +# # add drawing of circuit. -# -# Then, we can look at the probability of finding the output wave function in the computational basis state :math:`\ket{\mathrb{x}}` expressed as -# +# +# Then, we can look at the probability of finding the output wave function in the computational basis state +# :math:`\ket{\mathrb{x}}` expressed as +# # .. math:: # P_\theta(\mathrb{x}) = \norm*{ \bra{\mathrb{x}}\ket{\psi(\theta)}}^2 -# -# We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter vector :math:`\theta` in order to obtain the wave function that best approximates the target distribution. In other words, we can formulate this problem as the minimization -# +# +# We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter +# vector :math:`\theta` in order to obtain the wave function that best approximates the target distribution. +# In other words, we can formulate this problem as the minimization +# # .. math:: # min_{\theta} C(P_\theta(\mathrb{x})), -# -# where :math:`C` is the cost function to be optimized, which can take different forms based on the specific scenario, with the common denominator being that all of them should quantify the difference between the target probability and the probability distribution obtained from the quantum circuit. Due to the nature of the finite sampling used to estimate the distribution, analogous to what is done in classsical generative machine learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. -# +# +# where :math:`C` is the cost function to be optimized, which can take different forms based on the specific +# scenario, with the common denominator being that all of them should quantify the difference between the target +# probability and the probability distribution obtained from the quantum circuit. Due to the nature of the finite +# sampling used to estimate the distribution, analogous to what is done in classsical generative machine +# learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. +# # :math:: # C(\theta) = \sum_\mathrb{x} P_D(\mathrb{x}) ln \left ( \frac{P_D(\mathrb{x})}{P_\theta(\mathrb{x})} \right) -# -# +# +# # Tensor Network Ansatz # --------------------------- -# The algorithm presented in [#Benedetti]_, proposes the use of a hardware-efficient ansatz to prepare the probability distriubtion using a quantum circuit. However, in this work we take inspiration from previous approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. In particular, we take into consideration the local correlations of the data, and employ the MPS and TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ for a deeper study of these ansätze. -# +# The algorithm presented in [#Benedetti]_, proposes the use of a hardware-efficient ansatz to prepare +# the probability distriubtion using a quantum circuit. However, in this work we take inspiration from previous +# approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ +# and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor +# networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. +# In particular, we take into consideration the local correlations of the data, and employ the MPS and +# TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ +# for a deeper study of these ansätze. +# # # Pennylane implementation # --------------------------- -# +# For this demo, we need a bit of an extra help from `another repo `_ that +# will allow us to generate the dataset needed in this tutorial: +# +# .. code-block:: bash +# +# git clone https://github.com/XanaduAI/qml-benchmarks.git +# cd qml-benchmarks +# pip install . +# +# With that out of the way, we can start by importing what we need + +import pennylane as qml +from pennylane import numpy as np +from qml_benchmarks.data.bars_and_stripes import generate_bars_and_stripes +from tqdm import tqdm +import matplotlib.pyplot as plt + +# We then configure our random seed and setup some global variables that we will need for our experiments +np.random.seed(1) +dev = qml.device("default.qubit", wires=16) + +QUBITS = 16 +DATASET_SIZE = 1000 +TRAINING_ITERATIONS = 50 + +MPS_DATA_SHAPE = (qml.MPS.get_n_blocks(range(QUBITS), 2), 6) +TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, 6) + + +# For generating our dataset, which in our case is the Bar and Stripes dataset, we declare the following function: +def prepare_dataset(size, rows, cols): + X, _ = generate_bars_and_stripes(size, rows, cols, noise_std=0.0) + + # We need to transform the dataset from the {-1, 1} realm + # to the binary {0, 1} for easier processing + X += 1 + X //= 2 + + # Then we need to flatten the dataset + X = X.squeeze().reshape(X.shape[0], -1) + + # Finally, we need to determine the integer value + # of the instances and calculate their empirical probabilities + # The integer representation will allow for easy access of the + # required probabilities from the simulation + unique_elems, true_probs = np.unique(X, return_counts=True, axis=0) + idxs = unique_elems.dot(1 << np.arange(unique_elems.shape[-1] - 1, -1, -1)).astype( + np.int32 + ) + + return idxs, true_probs / size + + +# Note that for this demo, we assume that the underlying true probability of the dataset +# (which is a uniform probability for all elements) is unknown. Rather, we calculate an empirical probability from +# the samples generated by the `generate_bars_and_stripes` function. +# +# Next, we build our circuits for both the MPS and TTN ansätze: + + +def block(weights, wires): + qml.Rot(weights[0], weights[1], weights[2], wires=wires[0]) + qml.Rot(weights[3], weights[4], weights[5], wires=wires[1]) + + qml.CNOT(wires=wires) + + +@qml.qnode(dev) +def qcbm_circuit_mps(template_weights): + qml.MPS( + wires=range(QUBITS), + n_block_wires=2, + block=block, + n_params_block=6, + template_weights=template_weights, + ) + + return qml.probs() + + +@qml.qnode(dev) +def qcbm_circuit_ttn(template_weights): + # We need an adjoint here to reflect the circuit, + # such that the leaves of the TTN are at the measurement, + # more faithfully mimicking a TTN. + qml.adjoint( + qml.TTN( + wires=range(QUBITS), + n_block_wires=2, + block=block, + n_params_block=6, + template_weights=template_weights, + ) + ) + + return qml.probs() + + +# You will notice that we do not need to embed any data into the circuit, since QCBMs are generative model! +# Any interaction with our dataset will take place in the cost function. + + +# Now, we define our loss, which, as mentioned before, will be the KL-Divergence loss: +def kl_div(p, q): + return np.sum(q * np.log(q / p)) + + +# We are now ready to train some circuits! Let's generate our dataset first and prepare the optimizer. +idxs, true_probs = prepare_dataset(DATASET_SIZE, 4, 4) +optimizer = qml.AdamOptimizer() + + +# Let's start with the MPS circuit: +def cost_fn_mps(weights, idxs, true_probs): + probs = qcbm_circuit_mps(weights) + pred_probs = probs[idxs] + return kl_div(pred_probs, true_probs) + + +mps_weights_init = np.random.random(size=MPS_DATA_SHAPE) +mps_weights = mps_weights_init + +mps_costs = [] +for it in (pbar := tqdm(range(TRAINING_ITERATIONS))): + mps_weights = optimizer.step( + cost_fn_mps, mps_weights, idxs=idxs, true_probs=true_probs + ) + + current_cost = cost_fn_mps(mps_weights, idxs, true_probs) + + mps_costs.append(current_cost) + + pbar.set_postfix_str(f"KL Loss: {current_cost:.3f}") + +# Now we do the same for the TTN network, resetting the optimizer first. +optimizer.reset() + + +def cost_fn_ttn(weights, idxs, true_probs): + probs = qcbm_circuit_ttn(weights) + pred_probs = probs[idxs] + return kl_div(pred_probs, true_probs) + + +ttn_weights_init = np.random.random(size=TTN_DATA_SHAPE) +ttn_weights = ttn_weights_init + +ttn_costs = [] +for it in (pbar := tqdm(range(TRAINING_ITERATIONS))): + ttn_weights = optimizer.step( + cost_fn_ttn, ttn_weights, idxs=idxs, true_probs=true_probs + ) + + current_cost = cost_fn_ttn(ttn_weights, idxs, true_probs) + + ttn_costs.append(current_cost) + + pbar.set_postfix_str(f"KL Loss: {current_cost:.3f}") + +# Let's now plot the loss curves of the experiments against each other + +plt.plot(range(TRAINING_ITERATIONS), mps_costs, ".b", label="MPS Losses") +plt.plot(range(TRAINING_ITERATIONS), ttn_costs, ".g", label="TTN Losses") +plt.xlabel("Iteration #", fontsize=16) +plt.ylabel("KL Loss", fontsize=16) +plt.legend() +plt.show() + +# # References # ^^^^^^^^^^ # @@ -109,7 +312,8 @@ # URL ``__ - - - -I can then explain what are generative models generally, how born machine is one model possible, and how this has been attempted by using tensor networks. On the other hand it has also been attempted with quantum circuits, and here we combine both methods. I can say "quantum circuits are a particular instance of tensor networks, and therefore there is a natural connection" (cite the diagrammatic representation) +# I can then explain what are generative models generally, how born machine is one model possible, +# and how this has been attempted by using tensor networks. On the other hand it has also been +# attempted with quantum circuits, and here we combine both methods. I can say "quantum circuits are +# a particular instance of tensor networks, and therefore there is a natural connection" +# (cite the diagrammatic representation) From c755ccc989f348379f0be898310055be850f56ec Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Thu, 9 May 2024 18:16:42 -0400 Subject: [PATCH 05/31] merge code changes --- .../generative_discriminative.jpg | Bin 0 -> 136087 bytes .../qcbm_tensor_network/quantum_circuit.jpg | Bin 0 -> 151126 bytes .../tensor_network_wavefunction.jpg | Bin 0 -> 215314 bytes demonstrations/tutorial_qcbm.py | 20 ++++++++++++------ 4 files changed, 13 insertions(+), 7 deletions(-) create mode 100644 _static/demonstration_assets/qcbm_tensor_network/generative_discriminative.jpg create mode 100644 _static/demonstration_assets/qcbm_tensor_network/quantum_circuit.jpg create mode 100644 _static/demonstration_assets/qcbm_tensor_network/tensor_network_wavefunction.jpg diff --git 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zgF$vwMH|0>YE#DsEbLAKqIC^5^4@|MzTSVjs1#NLU=PC-R$c^-9u1CBOUkCk*Ixj9 z{QZT{xUmxYh};iY#uHDK(Jjx}0xplx56GqLwhF1{(<3OKQ+{?x8?6Kz1^eOnT+2rS zJpgPSAH3HD<5P`mqHT5&Q0y+PxqVY^lftWfPYvte6@jLSgmVnW#h6fy$@?$F7yc`8 zhCi?WKcdC|z Date: Fri, 10 May 2024 09:32:17 -0400 Subject: [PATCH 11/31] update references format on qcbm tutorial --- demonstrations/tutorial_qcbm.py | 42 ++++++++++++++------------------- 1 file changed, 18 insertions(+), 24 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 47e275e50c..c86eac9848 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -295,41 +295,35 @@ def cost_fn_ttn(weights, idxs, true_probs): ############################################################################## # References -# ^^^^^^^^^^ +# ---------- # # .. [#Benedetti] -# M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, -# "A generative modeling approach for benchmarking and training shallow quantum circuits", -# npj Quantum Information, 2019 +# M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz. +# "A generative modeling approach for benchmarking and training shallow quantum circuits", +# ``__, 2019. # # .. [#Cheng] -# S. Cheng, L. Wang, T. Xiang, and P. Zhang, -# *Physical Review B* **99**, 15 (2019), ISSN 2469-9969, -# URL ``__ +# Song Cheng, Lei Wang, Tao Xiang, and Pan Zhang. "Tree tensor networks for generative modeling" +# ``__, 2019. # # .. [#Ferris] -# A. J. Ferris and G. Vidal, -# *Physical Review B* **85**, 16 (2012), ISSN 1550-235X, -# URL ``__ +# Andrew J. Ferris and Guifre Vidal. "Perfect sampling with unitary tensor networks", +# ``__, 2020. # # .. [#Ballarin] -# M. Ballarin, P. Silvi, S. Montangero, and D. Jaschke, -# "Optimal sampling of tensor networks targeting wave function's fast decaying tails," (2024), -# arXiv:2401.10330 [quant-ph], -# URL ``__ +# Marco Ballarin, Pietro Silvi, Simone Montangero, and Daniel Jaschke. +# "Optimal sampling of tensor networks targeting wave function's fast decaying tails", +# ``__, 2024. # # .. [#Harrow] -# A. W. Harrow and A. Montanaro, -# *Nature* **549**, 7671, 203–209 (2017), ISSN 1476-4687, -# URL ``__ +# Aram W. Harrow & Ashley Montanaro. "Quantum computational supremacy", +# ``__, 2017. # # .. [#Goodfellow] -# I. Goodfellow, Y. Bengio, and A. Courville, -# *Deep Learning* (2016), -# MIT Press, -# URL ``__ +# Ian Goodfellow, Yoshua Bengio, and Aaron Courville. "Deep Learning", +# ``__, 2016. # # .. [#Han] -# Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang, -# *Physical Review X* **8**, 3 (2018), ISSN 2160-3308, -# URL ``__ +# Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang. +# "Unsupervised Generative Modeling Using Matrix Product States", +# ``__, 2018. From 51dbb13d54146ee50396bdd1bb50ecdddee7a159 Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Fri, 10 May 2024 09:34:41 -0400 Subject: [PATCH 12/31] minor fixes to math and spacing --- demonstrations/tutorial_qcbm.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index c86eac9848..36d0b8ff05 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -73,7 +73,7 @@ # # Then, we can look at the probability of finding the output wave function in the computational basis state # :math:`\ket{\mathbf{x}}` expressed as -# +# # .. math:: # P_\theta(\mathbf{x}) = \lVert\bra{\mathbf{x}}\ket{\psi(\theta)}\rVert^2 # @@ -90,7 +90,7 @@ # sampling used to estimate the distribution, analogous to what is done in classsical generative machine # learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. # -# :math:: +# .. math:: # C(\theta) = \sum_{\mathbf{x}} P_D(\mathbf{x}) \ln \left ( \frac{P_D(\mathbf{x})}{P_\theta(\mathbf{x})} \right) # # @@ -112,7 +112,7 @@ # :align: center # :width: 50 % # -# +# # Pennylane implementation # --------------------------- # For this demo, we need a bit of an extra help from `another repo `_ that @@ -219,9 +219,9 @@ def qcbm_circuit_ttn(template_weights): ############################################################################## # You will notice that we do not need to embed any data into the circuit, since QCBMs are generative model! # Any interaction with our dataset will take place in the cost function. +# Now, we define our loss, which, as mentioned before, will be the KL-Divergence loss: -# Now, we define our loss, which, as mentioned before, will be the KL-Divergence loss: def kl_div(p, q): return np.sum(q * np.log(q / p)) From 09b795cd504ce8994746b0edf303aa0d6c230bcc Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Fri, 10 May 2024 09:42:19 -0400 Subject: [PATCH 13/31] missing pluralization --- demonstrations/tutorial_qcbm.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 36d0b8ff05..4da6b07eb0 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -217,7 +217,7 @@ def qcbm_circuit_ttn(template_weights): ############################################################################## -# You will notice that we do not need to embed any data into the circuit, since QCBMs are generative model! +# You will notice that we do not need to embed any data into the circuit, since QCBMs are generative models! # Any interaction with our dataset will take place in the cost function. # Now, we define our loss, which, as mentioned before, will be the KL-Divergence loss: @@ -299,8 +299,8 @@ def cost_fn_ttn(weights, idxs, true_probs): # # .. [#Benedetti] # M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz. -# "A generative modeling approach for benchmarking and training shallow quantum circuits", -# ``__, 2019. +# "A generative modeling approach for benchmarking and training shallow quantum circuits", +# ``__, 2019. # # .. [#Cheng] # Song Cheng, Lei Wang, Tao Xiang, and Pan Zhang. "Tree tensor networks for generative modeling" @@ -320,10 +320,10 @@ def cost_fn_ttn(weights, idxs, true_probs): # ``__, 2017. # # .. [#Goodfellow] -# Ian Goodfellow, Yoshua Bengio, and Aaron Courville. "Deep Learning", +# Ian Goodfellow, Yoshua Bengio, and Aaron Courville. "Deep Learning", # ``__, 2016. # # .. [#Han] -# Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang. -# "Unsupervised Generative Modeling Using Matrix Product States", +# Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang. +# "Unsupervised Generative Modeling Using Matrix Product States", # ``__, 2018. From 21af5c1d4b141b9ecba90b7f98c5f909b8969284 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Fri, 10 May 2024 10:09:05 -0400 Subject: [PATCH 14/31] fix qc image size in qcbm tutorial --- demonstrations/tutorial_qcbm.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 4da6b07eb0..3388a5f853 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -69,7 +69,7 @@ # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/quantum_circuit.jpg # :align: center -# :height: 300 +# :height: 150 # # Then, we can look at the probability of finding the output wave function in the computational basis state # :math:`\ket{\mathbf{x}}` expressed as From 016931564eb992c223fbfbf2ae8db98ac3fdf059 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Fri, 10 May 2024 10:09:40 -0400 Subject: [PATCH 15/31] update images of ansatze --- .../qcbm_tensor_network/mps_ansatz.jpg | Bin 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10:12:18 -0400 Subject: [PATCH 16/31] add paragraphs around mps and ttn ansatze --- demonstrations/tutorial_qcbm.py | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 3388a5f853..6ad63ab647 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -97,17 +97,21 @@ # Tensor Network Ansatz # --------------------------- # The algorithm presented in [#Benedetti]_, proposes the use of a hardware-efficient ansatz to prepare -# the probability distriubtion using a quantum circuit. However, in this work we take inspiration from previous +# the probability distribution using a quantum circuit. However, in this work we take inspiration from previous # approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ # and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor # networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. # In particular, we take into consideration the local correlations of the data, and employ the MPS and # TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ -# for a deeper study of these ansätze. +# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit takes looks as +# follows. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/ttn_ansatz.jpg # :align: center # :width: 50 % +# +# Analagously, converting an MPS tensor network into a quantum circuit would be done as shown in the following figure. +# # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/mps_ansatz.jpg # :align: center # :width: 50 % From daa3aac9cedac1908c9f88e28342094b0fc33dac Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Fri, 10 May 2024 10:14:02 -0400 Subject: [PATCH 17/31] Added metadata for QCBM TN demo --- demonstrations/tutorial_qcbm.metadata.json | 45 ++++++++++++++++++++++ 1 file changed, 45 insertions(+) create mode 100644 demonstrations/tutorial_qcbm.metadata.json diff --git a/demonstrations/tutorial_qcbm.metadata.json b/demonstrations/tutorial_qcbm.metadata.json new file mode 100644 index 0000000000..19860e7bd3 --- /dev/null +++ b/demonstrations/tutorial_qcbm.metadata.json @@ -0,0 +1,45 @@ +{ + "title": "QCBM with Tensor Networks Ansatz", + "authors": [ + { + "id": "ahmed_darwish" + }, + { + "id": "emiliano_godinez" + } + ], + "dateOfPublication": "", + "dateOfLastModification": "2024-05-10T00:00:00+00:00", + "categories": [ + "Quantum Machine Learning" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/external_libs/thumbnail_tutorial_external_libs.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/demonstration_assets/qcbm_tensor_network/ttn_ansatz.png" + } + ], + "seoDescription": "Learn how to implement a QCBM with Tensor Network ansatz.", + "doi": "", + "canonicalURL": "/qml/demos/tutorial_qcbm", + "references": [], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_quantum_gans", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_QGAN", + "weight": 1.0 + } + ] +} \ No newline at end of file From b59964072fe9b69a8bcce54a45722220efb88bdc Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Fri, 10 May 2024 10:16:49 -0400 Subject: [PATCH 18/31] minor changes to the image sizes --- demonstrations/tutorial_qcbm.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 6ad63ab647..938b64b932 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -69,7 +69,7 @@ # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/quantum_circuit.jpg # :align: center -# :height: 150 +# :width: 50% # # Then, we can look at the probability of finding the output wave function in the computational basis state # :math:`\ket{\mathbf{x}}` expressed as @@ -103,18 +103,18 @@ # networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. # In particular, we take into consideration the local correlations of the data, and employ the MPS and # TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ -# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit takes looks as +# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit takes looks as # follows. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/ttn_ansatz.jpg # :align: center -# :width: 50 % -# +# :width: 70 % +# # Analagously, converting an MPS tensor network into a quantum circuit would be done as shown in the following figure. -# +# # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/mps_ansatz.jpg # :align: center -# :width: 50 % +# :width: 70 % # # # Pennylane implementation From 9316cabce1c26b0424e64bcb63fb8dfe85619f2c Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Fri, 10 May 2024 10:21:39 -0400 Subject: [PATCH 19/31] Applied black with the correct line length --- demonstrations/tutorial_qcbm.py | 12 +++--------- 1 file changed, 3 insertions(+), 9 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 938b64b932..5bb8ea2aca 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -167,9 +167,7 @@ def prepare_dataset(size, rows, cols): # The integer representation will allow for easy access of the # required probabilities from the simulation unique_elems, true_probs = np.unique(X, return_counts=True, axis=0) - idxs = unique_elems.dot(1 << np.arange(unique_elems.shape[-1] - 1, -1, -1)).astype( - np.int32 - ) + idxs = unique_elems.dot(1 << np.arange(unique_elems.shape[-1] - 1, -1, -1)).astype(np.int32) return idxs, true_probs / size @@ -249,9 +247,7 @@ def cost_fn_mps(weights, idxs, true_probs): mps_costs = [] for it in range(TRAINING_ITERATIONS + 1): - mps_weights = optimizer.step( - cost_fn_mps, mps_weights, idxs=idxs, true_probs=true_probs - ) + mps_weights = optimizer.step(cost_fn_mps, mps_weights, idxs=idxs, true_probs=true_probs) current_cost = cost_fn_mps(mps_weights, idxs, true_probs) @@ -276,9 +272,7 @@ def cost_fn_ttn(weights, idxs, true_probs): ttn_costs = [] for it in range(TRAINING_ITERATIONS + 1): - ttn_weights = optimizer.step( - cost_fn_ttn, ttn_weights, idxs=idxs, true_probs=true_probs - ) + ttn_weights = optimizer.step(cost_fn_ttn, ttn_weights, idxs=idxs, true_probs=true_probs) current_cost = cost_fn_ttn(ttn_weights, idxs, true_probs) From f98e20e4ae42fbb7ba97504b55352c41100ddef1 Mon Sep 17 00:00:00 2001 From: Cristian Emiliano Godinez Ramirez <57567043+EmilianoG-byte@users.noreply.github.com> Date: Fri, 10 May 2024 15:01:05 -0400 Subject: [PATCH 20/31] Update demonstrations/tutorial_qcbm.py MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Jorge J. Martínez de Lejarza <61199780+gmlejarza@users.noreply.github.com> --- demonstrations/tutorial_qcbm.py | 7 ------- 1 file changed, 7 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 5bb8ea2aca..45a3cf4370 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -4,13 +4,6 @@ QCBM with Tensor Networks Ansatz =============== -.. meta:: - :property="og:description": Implementing the Quantum Circuit Born Machine (QCBM) using a tensor network ansatz - :property="og:image": https://pennylane.ai/qml/_static/demonstration_assets//qaoa_maxcut_partition.png - -.. related:: - -*Author: Ahmed Darwish and Emiliano Godinez — Posted: 08 May 2024. Last updated: 08 May 2024.* In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. """ From f18b22840695a9260eff232465e302e343fba7d1 Mon Sep 17 00:00:00 2001 From: Cristian Emiliano Godinez Ramirez <57567043+EmilianoG-byte@users.noreply.github.com> Date: Fri, 10 May 2024 15:01:55 -0400 Subject: [PATCH 21/31] Update demonstrations/tutorial_qcbm.py Co-authored-by: serene <150857977+asymptoticgains@users.noreply.github.com> --- demonstrations/tutorial_qcbm.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 45a3cf4370..d2a3e0bcba 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -49,7 +49,7 @@ # # The problem formulation starts by looking at the training dataset # :math:`\mathcal{D} = (\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \ldots, \mathbf{x}^{(D)})` made up of :math:`D` binary -# vectors of length :math:`N`. Each of this vectors have an associated probability of occurring within the data, +# vectors of length :math:`N`. Each of these vectors has an associated probability of occurring within the data, # resulting in the target probability distribution :math:`P_{\mathcal{D}}`. For a quantum circuit # with :math:`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational # states and the input vectors From 2552ea62a05b8342a64b805eec31cd289b11e4da Mon Sep 17 00:00:00 2001 From: Cristian Emiliano Godinez Ramirez <57567043+EmilianoG-byte@users.noreply.github.com> Date: Fri, 10 May 2024 15:04:24 -0400 Subject: [PATCH 22/31] Update demonstrations/tutorial_qcbm.py Co-authored-by: serene <150857977+asymptoticgains@users.noreply.github.com> --- demonstrations/tutorial_qcbm.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index d2a3e0bcba..0d971043db 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -30,7 +30,7 @@ # p(x) = \lVert\bra{x}\ket{\psi}\rVert^2 # # As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent -# the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product +# the wave function in terms of tensor networks classes. In particular, the ubiquitous classes of Matrix Product # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the # training data, this making them suitable candidates be employed in the generative model. # From 0ea96965e3b3b968279bc7bb3423c1541da35b33 Mon Sep 17 00:00:00 2001 From: Cristian Emiliano Godinez Ramirez <57567043+EmilianoG-byte@users.noreply.github.com> Date: Fri, 10 May 2024 15:06:47 -0400 Subject: [PATCH 23/31] Apply suggestions from code review MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: serene <150857977+asymptoticgains@users.noreply.github.com> Co-authored-by: Jorge J. Martínez de Lejarza <61199780+gmlejarza@users.noreply.github.com> --- demonstrations/tutorial_qcbm.py | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 0d971043db..f7a51258e4 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -32,7 +32,7 @@ # As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent # the wave function in terms of tensor networks classes. In particular, the ubiquitous classes of Matrix Product # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the -# training data, this making them suitable candidates be employed in the generative model. +# training data, thus making them suitable candidates be employed in the generative model. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/tensor_network_wavefunction.jpg # :align: center @@ -89,14 +89,14 @@ # # Tensor Network Ansatz # --------------------------- -# The algorithm presented in [#Benedetti]_, proposes the use of a hardware-efficient ansatz to prepare +# The algorithm presented in [#Benedetti]_ proposes the use of a hardware-efficient ansatz to prepare # the probability distribution using a quantum circuit. However, in this work we take inspiration from previous # approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ # and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor # networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. # In particular, we take into consideration the local correlations of the data, and employ the MPS and # TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ -# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit takes looks as +# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit looks as # follows. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/ttn_ansatz.jpg @@ -143,7 +143,7 @@ ############################################################################## -# For generating our dataset, which in our case is the Bar and Stripes dataset, we declare the following function: +# For generating our dataset, which in our case is the Bars and Stripes dataset, we declare the following function: def prepare_dataset(size, rows, cols): X, _ = generate_bars_and_stripes(size, rows, cols, noise_std=0.0) @@ -318,3 +318,5 @@ def cost_fn_ttn(weights, idxs, true_probs): # Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang. # "Unsupervised Generative Modeling Using Matrix Product States", # ``__, 2018. +# About the authors +# ---------------- From c74804c96e6bd9d975f33b0323fd54f469c73b40 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Fri, 10 May 2024 15:16:23 -0400 Subject: [PATCH 24/31] add suggestion of phrasing on wavefunctions --- demonstrations/tutorial_qcbm.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index f7a51258e4..0bcb42f41f 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -40,7 +40,7 @@ # # Tensor networks and Quantum Circuits # ----------------------- -# As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wavefunction +# As part of the generative model pipeline, it is necessary to draw finite samples from the distribution represented by the wavefunction # in order to approximate the target probability distribution. While many algorithms have been proposed to sample # tensor networks classes efficiently ([#Ferris]_, [#Ballarin]_), as suggested in [#Harrow]_, this task appears as # a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. @@ -318,5 +318,6 @@ def cost_fn_ttn(weights, idxs, true_probs): # Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang. # "Unsupervised Generative Modeling Using Matrix Product States", # ``__, 2018. +# # About the authors # ---------------- From 6b9bcb3405ba13517dfe8134dcd2b400b61423e0 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Fri, 10 May 2024 16:05:42 -0400 Subject: [PATCH 25/31] move comments out of functions --- demonstrations/tutorial_qcbm.py | 19 +++++++++---------- 1 file changed, 9 insertions(+), 10 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 0bcb42f41f..41cb877a52 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -113,7 +113,7 @@ # Pennylane implementation # --------------------------- # For this demo, we need a bit of an extra help from `another repo `_ that -# will allow us to generate the dataset needed in this tutorial: +# will allow us to generate the dataset used for training, i.e. the bars and stripes data set. # # .. code-block:: bash # @@ -129,7 +129,7 @@ import matplotlib.pyplot as plt ############################################################################## -# We then configure our random seed and setup some global variables that we will need for our experiments +# We then configure our random seed and setup the global variables that we will need for our experiments np.random.seed(1) dev = qml.device("default.qubit", wires=16) @@ -143,22 +143,19 @@ ############################################################################## -# For generating our dataset, which in our case is the Bars and Stripes dataset, we declare the following function: +# For generating our dataset, which in our case is the bars and stripes dataset, we declare the following function: def prepare_dataset(size, rows, cols): X, _ = generate_bars_and_stripes(size, rows, cols, noise_std=0.0) - # We need to transform the dataset from the {-1, 1} realm - # to the binary {0, 1} for easier processing + # We need to transform the dataset from the {-1, 1} + # to the binary {0, 1} range for easier processing X += 1 X //= 2 # Then we need to flatten the dataset X = X.squeeze().reshape(X.shape[0], -1) - # Finally, we need to determine the integer value - # of the instances and calculate their empirical probabilities - # The integer representation will allow for easy access of the - # required probabilities from the simulation + # Calculate integer representation unique_elems, true_probs = np.unique(X, return_counts=True, axis=0) idxs = unique_elems.dot(1 << np.arange(unique_elems.shape[-1] - 1, -1, -1)).astype(np.int32) @@ -166,9 +163,11 @@ def prepare_dataset(size, rows, cols): ############################################################################## +# The last part of this function calculates the integer representation of the instances, which we will give us access to the empirical probabilities from the simulation. +# # Note that for this demo, we assume that the underlying true probability of the dataset # (which is a uniform probability for all elements) is unknown. Rather, we calculate an empirical probability from -# the samples generated by the `generate_bars_and_stripes` function. +# the samples generated by the ``generate_bars_and_stripes`` function. # # Next, we build our circuits for both the MPS and TTN ansätze: From 26cd8365ffe1f5bbce58dcaaa31870ac0872d01a Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Sat, 11 May 2024 14:35:58 -0400 Subject: [PATCH 26/31] added faster jax-based code and more iterations --- demonstrations/tutorial_qcbm.py | 109 +++++++++++++++++++++----------- 1 file changed, 72 insertions(+), 37 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 41cb877a52..63ccf536fa 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -123,23 +123,26 @@ # # With that out of the way, we can start by importing what we need +from typing import Literal import pennylane as qml -from pennylane import numpy as np +from functools import partial from qml_benchmarks.data.bars_and_stripes import generate_bars_and_stripes import matplotlib.pyplot as plt +import jax.numpy as np +import jax +import optax ############################################################################## # We then configure our random seed and setup the global variables that we will need for our experiments -np.random.seed(1) dev = qml.device("default.qubit", wires=16) QUBITS = 16 DATASET_SIZE = 1000 -TRAINING_ITERATIONS = 50 +TRAINING_ITERATIONS = 100 -MPS_DATA_SHAPE = (qml.MPS.get_n_blocks(range(QUBITS), 2), 6) -TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, 6) +MPS_DATA_SHAPE = (qml.MPS.get_n_blocks(range(QUBITS), 2), 18) +TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, 18) ############################################################################## @@ -178,34 +181,28 @@ def block(weights, wires): qml.CNOT(wires=wires) + qml.Rot(weights[6], weights[7], weights[8], wires=wires[0]) + qml.Rot(weights[9], weights[10], weights[11], wires=wires[1]) -@qml.qnode(dev) -def qcbm_circuit_mps(template_weights): - qml.MPS( + qml.CNOT(wires=wires) + + qml.Rot(weights[12], weights[13], weights[14], wires=wires[0]) + qml.Rot(weights[15], weights[16], weights[17], wires=wires[1]) + + +@partial(jax.jit, static_argnums=(1,)) +@qml.qnode(dev, interface="jax") +def qcbm_circuit(template_weights, template_type: Literal["MPS", "TTN"]): + tn_ansatz = getattr(qml, template_type)( wires=range(QUBITS), n_block_wires=2, block=block, - n_params_block=6, + n_params_block=18, template_weights=template_weights, ) - return qml.probs() - - -@qml.qnode(dev) -def qcbm_circuit_ttn(template_weights): - # We need an adjoint here to reflect the circuit, - # such that the leaves of the TTN are at the measurement, - # more faithfully mimicking a TTN. - qml.adjoint( - qml.TTN( - wires=range(QUBITS), - n_block_wires=2, - block=block, - n_params_block=6, - template_weights=template_weights, - ) - ) + if template_type == "TTN": + qml.adjoint(tn_ansatz) return qml.probs() @@ -223,23 +220,29 @@ def kl_div(p, q): ############################################################################## # We are now ready to train some circuits! Let's generate our dataset first and prepare the optimizer. idxs, true_probs = prepare_dataset(DATASET_SIZE, 4, 4) -optimizer = qml.AdamOptimizer() +learning_rate = 0.01 +optimizer = optax.adam(learning_rate) ############################################################################## # Let's start with the MPS circuit: def cost_fn_mps(weights, idxs, true_probs): - probs = qcbm_circuit_mps(weights) + probs = qcbm_circuit(weights, template_type="MPS") pred_probs = probs[idxs] return kl_div(pred_probs, true_probs) -mps_weights_init = np.random.random(size=MPS_DATA_SHAPE) +key = jax.random.PRNGKey(42) +mps_weights_init = jax.random.uniform(key=key, shape=MPS_DATA_SHAPE) mps_weights = mps_weights_init +opt_state = optimizer.init(mps_weights) + mps_costs = [] for it in range(TRAINING_ITERATIONS + 1): - mps_weights = optimizer.step(cost_fn_mps, mps_weights, idxs=idxs, true_probs=true_probs) + grads = jax.grad(cost_fn_mps)(mps_weights, idxs=idxs, true_probs=true_probs) + updates, opt_state = optimizer.update(grads, opt_state) + mps_weights = optax.apply_updates(mps_weights, updates) current_cost = cost_fn_mps(mps_weights, idxs, true_probs) @@ -250,21 +253,23 @@ def cost_fn_mps(weights, idxs, true_probs): ############################################################################## # Now we do the same for the TTN network, resetting the optimizer first. -optimizer.reset() +optimizer = optax.adam(learning_rate) def cost_fn_ttn(weights, idxs, true_probs): - probs = qcbm_circuit_ttn(weights) + probs = qcbm_circuit(weights, template_type="TTN") pred_probs = probs[idxs] return kl_div(pred_probs, true_probs) -ttn_weights_init = np.random.random(size=TTN_DATA_SHAPE) +ttn_weights_init = jax.random.uniform(key=key, shape=TTN_DATA_SHAPE) ttn_weights = ttn_weights_init ttn_costs = [] for it in range(TRAINING_ITERATIONS + 1): - ttn_weights = optimizer.step(cost_fn_ttn, ttn_weights, idxs=idxs, true_probs=true_probs) + grads = jax.grad(cost_fn_ttn)(ttn_weights, idxs=idxs, true_probs=true_probs) + updates, opt_state = optimizer.update(grads, opt_state) + ttn_weights = optax.apply_updates(ttn_weights, updates) current_cost = cost_fn_ttn(ttn_weights, idxs, true_probs) @@ -274,15 +279,45 @@ def cost_fn_ttn(weights, idxs, true_probs): print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") ############################################################################## -# Let's now plot the loss curves of the experiments against each other +# We can plot the loss curves of both models and see how their performance differs -plt.plot(range(TRAINING_ITERATIONS + 1), mps_costs, ".b", label="MPS Losses") -plt.plot(range(TRAINING_ITERATIONS + 1), ttn_costs, ".g", label="TTN Losses") + +plt.plot(range(TRAINING_ITERATIONS + 1), mps_costs, "-.b", label="MPS Losses") +plt.plot(range(TRAINING_ITERATIONS + 1), ttn_costs, "-.g", label="TTN Losses") plt.xlabel("Iteration #", fontsize=16) plt.ylabel("KL Loss", fontsize=16) plt.legend() plt.show() +############################################################################## +# Let's now generate some samples from our models and see how stripe-y they are: + + +def generate_and_plot(circuit_fn, weights, template): + probs = circuit_fn(weights, template) + generated_samples = jax.random.choice(key=key, a=len(probs), shape=(9,), p=probs) + generated_samples_bin = ( + (generated_samples.reshape(-1, 1) & (2 ** np.arange(QUBITS))) != 0 + ).astype(int) + + plt.figure(figsize=[3, 3]) + for i, sample in enumerate(generated_samples_bin): + plt.subplot(3, 3, (i % 9) + 1) + plt.imshow(np.reshape(sample[::-1], [4, 4]), cmap="gray") + plt.xticks([]) + plt.yticks([]) + + plt.show() + + +############################################################################## +# First, we generate samples from the MPS model +generate_and_plot(qcbm_circuit, mps_weights, "MPS") + +############################################################################## +# Then, we generate samples from the TTN model +generate_and_plot(qcbm_circuit, ttn_weights, "TTN") + ############################################################################## # References # ---------- From 54d483bb61df83e586336f5b0ae6b18f444c4904 Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Sat, 11 May 2024 16:41:40 -0400 Subject: [PATCH 27/31] Added conclusion, fixed several typos and math render error. Refactored the training code and added more explanation to several functions. --- demonstrations/tutorial_qcbm.py | 168 ++++++++++++++++++-------------- 1 file changed, 96 insertions(+), 72 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 63ccf536fa..1bddc5aa9b 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -5,7 +5,10 @@ =============== -In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. +In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by +Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_, to obtain the probability +distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane +to construct the model's ansatz. """ ############################################################################## @@ -20,17 +23,17 @@ # :align: center # :height: 300 # -# An important trait of the generative model that allows for this generation of new samples is rooted on its +# An important trait of the generative model that allows for this generation of new samples is rooted in its # ability to capture correlations present in the input data. Among the different models employed in the literature -# for generative machine learning, the so called "Born machine" model is based on representing the probability -# distribution :math:`p(x)` in terms of the amplitudes of the quantum wave function :math:`\ket{\psi}`, with the +# for generative machine learning, the so-called "Born machine" model is based on representing the probability +# distribution :math:`p(x)` in terms of the amplitudes of the quantum wavefunction :math:`\ket{\psi}`, with the # relation given by Born's rule # # .. math:: # p(x) = \lVert\bra{x}\ket{\psi}\rVert^2 # -# As done in [#Cheng]_ the efficient representation provided by tensor network ansätze invites us to represent -# the wave function in terms of tensor networks classes. In particular, the ubiquitous classes of Matrix Product +# As done in [#Cheng]_, the efficient representation provided by tensor network ansätze invites us to represent +# the wavefunction in terms of tensor networks classes. In particular, the ubiquitous classes of Matrix Product # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the # training data, thus making them suitable candidates be employed in the generative model. # @@ -42,15 +45,15 @@ # ----------------------- # As part of the generative model pipeline, it is necessary to draw finite samples from the distribution represented by the wavefunction # in order to approximate the target probability distribution. While many algorithms have been proposed to sample -# tensor networks classes efficiently ([#Ferris]_, [#Ballarin]_), as suggested in [#Harrow]_, this task appears as -# a suitable candidate to attempt and achieve quantum advantage in Near Intermediate Scale Quantum (NISQ) devices. +# from tensor networks efficiently ([#Ferris]_, [#Ballarin]_), this task appears as a suitable candidate to attempt and +# achieve quantum advantage in Noisy Intermediate-Scale Quantum (NISQ) devices, as suggested in [#Harrow]_. # As presented in [#Benedetti]_, this approach employing quantum circuits to model the probabililty distribution is # known as the Quantum Circuit Born Machine (QCBM). # # The problem formulation starts by looking at the training dataset -# :math:`\mathcal{D} = (\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \ldots, \mathbf{x}^{(D)})` made up of :math:`D` binary +# :math:`\mathfrak{D} = (\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \ldots, \mathbf{x}^{(D)})` made up of :math:`D` binary # vectors of length :math:`N`. Each of these vectors has an associated probability of occurring within the data, -# resulting in the target probability distribution :math:`P_{\mathcal{D}}`. For a quantum circuit +# resulting in the target probability distribution :math:`P_{\mathfrak{D}}`. For a quantum circuit # with :math:`N` qubits, this formulation gives rise to the one-to-one mapping betweeen the computational # states and the input vectors # @@ -64,15 +67,15 @@ # :align: center # :width: 50% # -# Then, we can look at the probability of finding the output wave function in the computational basis state +# Then, we can look at the probability of finding the output wavefunction in the computational basis state # :math:`\ket{\mathbf{x}}` expressed as # # .. math:: # P_\theta(\mathbf{x}) = \lVert\bra{\mathbf{x}}\ket{\psi(\theta)}\rVert^2 # # We can then use this quantity to define a cost function to be minimized by iteratively optimizing the parameter -# vector :math:`\theta` in order to obtain the wave function that best approximates the target distribution. -# In other words, we can formulate this problem as the minimization +# vector :math:`\theta` in order to obtain the wavefunction that best approximates the target distribution. +# In other words, we can formulate this problem as the minimization of # # .. math:: # \min_{\theta} C(P_\theta(\mathbf{x})), @@ -81,29 +84,29 @@ # scenario, with the common denominator being that all of them should quantify the difference between the target # probability and the probability distribution obtained from the quantum circuit. Due to the nature of the finite # sampling used to estimate the distribution, analogous to what is done in classsical generative machine -# learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. +# learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence: # # .. math:: -# C(\theta) = \sum_{\mathbf{x}} P_D(\mathbf{x}) \ln \left ( \frac{P_D(\mathbf{x})}{P_\theta(\mathbf{x})} \right) +# C(\theta) = \sum_{\mathbf{x}} P_\mathfrak{D}(\mathbf{x}) \ln \left ( \frac{P_D(\mathbf{x})}{P_\theta(\mathbf{x})} \right) # # # Tensor Network Ansatz # --------------------------- # The algorithm presented in [#Benedetti]_ proposes the use of a hardware-efficient ansatz to prepare # the probability distribution using a quantum circuit. However, in this work we take inspiration from previous -# approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ +# approaches to generative modelling using tensor networks to represent the wavefunction, as done in [#Han]_ # and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor # networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. # In particular, we take into consideration the local correlations of the data, and employ the MPS and -# TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ -# for a deeper study of these ansätze. The conversion between the TTN class into a quantum circuit looks as +# TTN circuit ansatz implemented in Pennylane. See `this tutorial `_ +# for a clearer understanding of these ansätze. The conversion between a TTN of bond dimension 2 into a quantum circuit looks as # follows. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/ttn_ansatz.jpg # :align: center # :width: 70 % # -# Analagously, converting an MPS tensor network into a quantum circuit would be done as shown in the following figure. +# Analagously, converting a bond dimension 2 MPS tensor network into a quantum circuit would be done as shown in the following figure. # # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/mps_ansatz.jpg # :align: center @@ -133,20 +136,24 @@ import optax ############################################################################## -# We then configure our random seed and setup the global variables that we will need for our experiments +# We then configure our random seed and setup the constants that we will need for our experiments dev = qml.device("default.qubit", wires=16) +key = jax.random.PRNGKey(1) QUBITS = 16 DATASET_SIZE = 1000 TRAINING_ITERATIONS = 100 +N_PARAMS_PER_BLOCK = 15 +LEARNING_RATE = 0.01 -MPS_DATA_SHAPE = (qml.MPS.get_n_blocks(range(QUBITS), 2), 18) -TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, 18) + +MPS_DATA_SHAPE = (qml.MPS.get_n_blocks(range(QUBITS), 2), N_PARAMS_PER_BLOCK) +TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, N_PARAMS_PER_BLOCK) ############################################################################## -# For generating our dataset, which in our case is the bars and stripes dataset, we declare the following function: +# For generating our dataset, which in our case is the bars and stripes dataset, we declare the following function. def prepare_dataset(size, rows, cols): X, _ = generate_bars_and_stripes(size, rows, cols, noise_std=0.0) @@ -158,7 +165,6 @@ def prepare_dataset(size, rows, cols): # Then we need to flatten the dataset X = X.squeeze().reshape(X.shape[0], -1) - # Calculate integer representation unique_elems, true_probs = np.unique(X, return_counts=True, axis=0) idxs = unique_elems.dot(1 << np.arange(unique_elems.shape[-1] - 1, -1, -1)).astype(np.int32) @@ -166,28 +172,29 @@ def prepare_dataset(size, rows, cols): ############################################################################## -# The last part of this function calculates the integer representation of the instances, which we will give us access to the empirical probabilities from the simulation. -# -# Note that for this demo, we assume that the underlying true probability of the dataset -# (which is a uniform probability for all elements) is unknown. Rather, we calculate an empirical probability from -# the samples generated by the ``generate_bars_and_stripes`` function. +# The last part of the function calculates the empirical probabilities of the generated samples +# from the helper function `generate_bars_and_stripes`. Note that we also need the integer value +# of the generated samples to use as an index for the probability vectors that are going to be +# extracted from our circuits. # -# Next, we build our circuits for both the MPS and TTN ansätze: +# Next, we build our circuits for both the MPS and TTN ansätze. For the main building block of each node +# in the ansatz, we are going to be using an SU(4) block, since it can express any 2-qubit unitary. -def block(weights, wires): +def su4_block(weights, wires): qml.Rot(weights[0], weights[1], weights[2], wires=wires[0]) qml.Rot(weights[3], weights[4], weights[5], wires=wires[1]) qml.CNOT(wires=wires) - qml.Rot(weights[6], weights[7], weights[8], wires=wires[0]) - qml.Rot(weights[9], weights[10], weights[11], wires=wires[1]) + qml.RZ(weights[6], wires=wires[1]) + qml.RY(weights[7], wires=wires[1]) + qml.RX(weights[8], wires=wires[1]) qml.CNOT(wires=wires) - qml.Rot(weights[12], weights[13], weights[14], wires=wires[0]) - qml.Rot(weights[15], weights[16], weights[17], wires=wires[1]) + qml.Rot(weights[9], weights[10], weights[11], wires=wires[0]) + qml.Rot(weights[12], weights[13], weights[14], wires=wires[1]) @partial(jax.jit, static_argnums=(1,)) @@ -196,8 +203,8 @@ def qcbm_circuit(template_weights, template_type: Literal["MPS", "TTN"]): tn_ansatz = getattr(qml, template_type)( wires=range(QUBITS), n_block_wires=2, - block=block, - n_params_block=18, + block=su4_block, + n_params_block=N_PARAMS_PER_BLOCK, template_weights=template_weights, ) @@ -210,6 +217,16 @@ def qcbm_circuit(template_weights, template_type: Literal["MPS", "TTN"]): ############################################################################## # You will notice that we do not need to embed any data into the circuit, since QCBMs are generative models! # Any interaction with our dataset will take place in the cost function. +# +# You can also see how we are applying the adjoing operation on the template when using a TTN. +# This is a minor hack to mirror the ansatz. This is needed since for generation, we want the root +# of the tree to be at the beginning of the circuit, as described in [#Stoudenmire]_. +# +# One final thing to notice is the number of qubits each block will be affecting. Our choice of 2 here +# reflects the expressivity of the model, since it is directly correlated to the bond dimensions of +# the tensor networks as illustrated in the previous section. For larger, more expressive bond dimensions, +# gates interacting with more qubits is needed, but that would not necessarily be hardware-efficient on the current NISQ devices. +# # Now, we define our loss, which, as mentioned before, will be the KL-Divergence loss: @@ -218,10 +235,29 @@ def kl_div(p, q): ############################################################################## -# We are now ready to train some circuits! Let's generate our dataset first and prepare the optimizer. +# We are now ready to train some circuits! Let's generate our dataset first and prepare the training function. idxs, true_probs = prepare_dataset(DATASET_SIZE, 4, 4) -learning_rate = 0.01 -optimizer = optax.adam(learning_rate) +optimizer = optax.adam(LEARNING_RATE) + + +def train_circuit(cost_fn, init_weights, optimizer): + opt_state = optimizer.init(init_weights) + weights = init_weights + + costs = [] + for it in range(TRAINING_ITERATIONS + 1): + grads = jax.grad(cost_fn)(weights, idxs=idxs, true_probs=true_probs) + updates, opt_state = optimizer.update(grads, opt_state) + weights = optax.apply_updates(weights, updates) + + current_cost = cost_fn(weights, idxs, true_probs) + + costs.append(current_cost) + + if it % 10 == 0: + print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") + + return costs, weights ############################################################################## @@ -232,28 +268,13 @@ def cost_fn_mps(weights, idxs, true_probs): return kl_div(pred_probs, true_probs) -key = jax.random.PRNGKey(42) mps_weights_init = jax.random.uniform(key=key, shape=MPS_DATA_SHAPE) -mps_weights = mps_weights_init -opt_state = optimizer.init(mps_weights) - -mps_costs = [] -for it in range(TRAINING_ITERATIONS + 1): - grads = jax.grad(cost_fn_mps)(mps_weights, idxs=idxs, true_probs=true_probs) - updates, opt_state = optimizer.update(grads, opt_state) - mps_weights = optax.apply_updates(mps_weights, updates) - - current_cost = cost_fn_mps(mps_weights, idxs, true_probs) - - mps_costs.append(current_cost) - - if it % 10 == 0: - print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") +mps_costs, mps_weights = train_circuit(cost_fn_mps, mps_weights_init, optimizer) ############################################################################## # Now we do the same for the TTN network, resetting the optimizer first. -optimizer = optax.adam(learning_rate) +optimizer = optax.adam(LEARNING_RATE) def cost_fn_ttn(weights, idxs, true_probs): @@ -263,25 +284,12 @@ def cost_fn_ttn(weights, idxs, true_probs): ttn_weights_init = jax.random.uniform(key=key, shape=TTN_DATA_SHAPE) -ttn_weights = ttn_weights_init - -ttn_costs = [] -for it in range(TRAINING_ITERATIONS + 1): - grads = jax.grad(cost_fn_ttn)(ttn_weights, idxs=idxs, true_probs=true_probs) - updates, opt_state = optimizer.update(grads, opt_state) - ttn_weights = optax.apply_updates(ttn_weights, updates) - - current_cost = cost_fn_ttn(ttn_weights, idxs, true_probs) - ttn_costs.append(current_cost) - - if it % 10 == 0: - print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") +ttn_costs, ttn_weights = train_circuit(cost_fn_ttn, ttn_weights_init, optimizer) ############################################################################## # We can plot the loss curves of both models and see how their performance differs - plt.plot(range(TRAINING_ITERATIONS + 1), mps_costs, "-.b", label="MPS Losses") plt.plot(range(TRAINING_ITERATIONS + 1), ttn_costs, "-.g", label="TTN Losses") plt.xlabel("Iteration #", fontsize=16) @@ -290,6 +298,9 @@ def cost_fn_ttn(weights, idxs, true_probs): plt.show() ############################################################################## +# As expected, the TTN ansatz is able to achieve a smaller loss compared to the MPS one. +# This is due to the topology of the TTN ansatz able to capture non-adjacent correlations +# in the data thanks to its tree structure. # Let's now generate some samples from our models and see how stripe-y they are: @@ -318,6 +329,14 @@ def generate_and_plot(circuit_fn, weights, template): # Then, we generate samples from the TTN model generate_and_plot(qcbm_circuit, ttn_weights, "TTN") +############################################################################## +# We can see that for both models, the generated samples are not perfect, which is +# a sign that our models are not expressive enough for the task at hand. As explained before, +# one can play around with blocks affecting more qubits at once which would allow the models +# to capture the more minute correlations and create better entanglement in the model. +# One can also experiment with more standard topologies such as the `MERA ansatz `_ +# or the PEPS topology, which is very suitable for 2D datasets such as ours. + ############################################################################## # References # ---------- @@ -337,7 +356,7 @@ def generate_and_plot(circuit_fn, weights, template): # # .. [#Ballarin] # Marco Ballarin, Pietro Silvi, Simone Montangero, and Daniel Jaschke. -# "Optimal sampling of tensor networks targeting wave function's fast decaying tails", +# "Optimal sampling of tensor networks targeting wavefunction's fast decaying tails", # ``__, 2024. # # .. [#Harrow] @@ -353,5 +372,10 @@ def generate_and_plot(circuit_fn, weights, template): # "Unsupervised Generative Modeling Using Matrix Product States", # ``__, 2018. # +# .. [#Stoudenmire] +# Huggins, William and Patil, Piyush and Mitchell, Bradley and Whaley, K Birgitta and Stoudenmire, E Miles +# "Towards quantum machine learning with tensor networks", +# ``__, 2018. +# # About the authors # ---------------- From c835fc2c059bf8ea73f9496974c9a323947d6e3f Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Mon, 5 Aug 2024 11:25:07 -0400 Subject: [PATCH 28/31] rename python and json files to avoid conflicts on master --- ...utorial_qcbm.metadata.json => tutorial_qcbm_tn.metadata.json} | 0 demonstrations/{tutorial_qcbm.py => tutorial_qcbm_tn.py} | 0 test-results/sphinx-gallery/junit.xml | 1 + 3 files changed, 1 insertion(+) rename demonstrations/{tutorial_qcbm.metadata.json => tutorial_qcbm_tn.metadata.json} (100%) rename demonstrations/{tutorial_qcbm.py => tutorial_qcbm_tn.py} (100%) create mode 100644 test-results/sphinx-gallery/junit.xml diff --git a/demonstrations/tutorial_qcbm.metadata.json b/demonstrations/tutorial_qcbm_tn.metadata.json similarity index 100% rename from demonstrations/tutorial_qcbm.metadata.json rename to demonstrations/tutorial_qcbm_tn.metadata.json diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm_tn.py similarity index 100% rename from demonstrations/tutorial_qcbm.py rename to demonstrations/tutorial_qcbm_tn.py diff --git a/test-results/sphinx-gallery/junit.xml b/test-results/sphinx-gallery/junit.xml new file mode 100644 index 0000000000..64eb9f3cab --- /dev/null +++ b/test-results/sphinx-gallery/junit.xml @@ -0,0 +1 @@ + \ No newline at end of file From cb62f8df1dcf32b80cf7f9301f4fda1b68b0f875 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Mon, 5 Aug 2024 11:29:25 -0400 Subject: [PATCH 29/31] update dateofpublication --- demonstrations/tutorial_qcbm_tn.metadata.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_qcbm_tn.metadata.json b/demonstrations/tutorial_qcbm_tn.metadata.json index 19860e7bd3..171eef99b4 100644 --- a/demonstrations/tutorial_qcbm_tn.metadata.json +++ b/demonstrations/tutorial_qcbm_tn.metadata.json @@ -8,7 +8,7 @@ "id": "emiliano_godinez" } ], - "dateOfPublication": "", + "dateOfPublication": "2024-05-10T00:00:00+00:00", "dateOfLastModification": "2024-05-10T00:00:00+00:00", "categories": [ "Quantum Machine Learning" From 78b5460eb1653bb9d629959a970690c830194bb3 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Mon, 5 Aug 2024 17:08:29 -0400 Subject: [PATCH 30/31] add qml-benchmarks to dependecies --- pyproject.toml | 1 + 1 file changed, 1 insertion(+) diff --git a/pyproject.toml b/pyproject.toml index d7d26ab02f..f4ffbaac36 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -73,6 +73,7 @@ qiskit = ">=1.0.0" qiskit-aer = ">=0.14.0" sphinxcontrib-applehelp = "1.0.8" sphinx-gallery = "<=0.12.2" +qml-benchmarks = { git = "https://github.com/XanaduAI/qml-benchmarks.git", tag = "v0.1" } # Install a difference version of torch from PyPI as the one from PyTorch repo is not compatible with MacOS From 5286491b2724fc5383f05adad80556df480d0dc3 Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Mon, 5 Aug 2024 17:13:35 -0400 Subject: [PATCH 31/31] update lockfile --- poetry.lock | 35 +++++++++++++++++++++++++++++++---- 1 file changed, 31 insertions(+), 4 deletions(-) diff --git a/poetry.lock b/poetry.lock index 79fb320e14..51ca5e7dfe 100644 --- a/poetry.lock +++ b/poetry.lock @@ -2040,8 +2040,6 @@ files = [ {file = "frozendict-2.4.4-cp39-cp39-musllinux_1_1_x86_64.whl", hash = "sha256:d13b4310db337f4d2103867c5a05090b22bc4d50ca842093779ef541ea9c9eea"}, {file = "frozendict-2.4.4-cp39-cp39-win_amd64.whl", hash = "sha256:b3b967d5065872e27b06f785a80c0ed0a45d1f7c9b85223da05358e734d858ca"}, {file = "frozendict-2.4.4-cp39-cp39-win_arm64.whl", hash = "sha256:4ae8d05c8d0b6134bfb6bfb369d5fa0c4df21eabb5ca7f645af95fdc6689678e"}, - {file = "frozendict-2.4.4-py311-none-any.whl", hash = "sha256:705efca8d74d3facbb6ace80ab3afdd28eb8a237bfb4063ed89996b024bc443d"}, - {file = "frozendict-2.4.4-py312-none-any.whl", hash = "sha256:d9647563e76adb05b7cde2172403123380871360a114f546b4ae1704510801e5"}, {file = "frozendict-2.4.4.tar.gz", hash = "sha256:3f7c031b26e4ee6a3f786ceb5e3abf1181c4ade92dce1f847da26ea2c96008c7"}, ] @@ -3102,7 +3100,6 @@ description = "Clang Python Bindings, mirrored from the official LLVM repo: http optional = false python-versions = "*" files = [ - {file = "libclang-18.1.1-1-py2.py3-none-macosx_11_0_arm64.whl", hash = "sha256:0b2e143f0fac830156feb56f9231ff8338c20aecfe72b4ffe96f19e5a1dbb69a"}, {file = "libclang-18.1.1-py2.py3-none-macosx_10_9_x86_64.whl", hash = "sha256:6f14c3f194704e5d09769108f03185fce7acaf1d1ae4bbb2f30a72c2400cb7c5"}, {file = "libclang-18.1.1-py2.py3-none-macosx_11_0_arm64.whl", hash = "sha256:83ce5045d101b669ac38e6da8e58765f12da2d3aafb3b9b98d88b286a60964d8"}, {file = "libclang-18.1.1-py2.py3-none-manylinux2010_x86_64.whl", hash = "sha256:c533091d8a3bbf7460a00cb6c1a71da93bffe148f172c7d03b1c31fbf8aa2a0b"}, @@ -5533,6 +5530,36 @@ requests-ntlm = ">=1.1.0" urllib3 = ">=1.21.1" websocket-client = ">=1.5.1" +[[package]] +name = "qml_benchmarks" +version = "0.1" +description = "A package to benchmark quantum machine learning models" +optional = false +python-versions = "*" +files = [] +develop = false + +[package.dependencies] +flax = "*" +jax = "*" +jaxlib = "*" +matplotlib = "*" +numpy = "*" +optax = "*" +pandas = "*" +pennylane = "*" +pyyaml = "*" +scikit_learn = "*" +scipy = "*" +seaborn = "*" +typing-extensions = "*" + +[package.source] +type = "git" +url = "https://github.com/XanaduAI/qml-benchmarks.git" +reference = "v0.1" +resolved_reference = "886648d47f4fff849f386ddcc41c3c76ac601b68" + [[package]] name = "quil" version = "0.10.0" @@ -8097,4 +8124,4 @@ files = [ [metadata] lock-version = "2.0" python-versions = "~3.10.0" -content-hash = "9d79a3c7864580ff575f8eed195b739cca63167e993e57f175bbe0127496a48f" +content-hash = "3331558e7fcf03e9e86a4065c99b19fdea70689c78daa598214377709f493f62"

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zl=^5&Rlkleq^VtgdKp^EG+U!~liKjy#Y`JW&2U&0K3e(ZkDyPrRHf9Lwnule@#=i6T$ V^Ix@>f4^t;SD*R6^ZCCI|1aTPXrTZA literal 0 HcmV?d00001 diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 3ee1b96c24..9f69cd9aac 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -22,8 +22,10 @@ # new data instances that follow the probability distribution of the input training data. This is in contrast # to other statistical models like the discriminative model, which allows us to "tell apart" the different instances # present in the the input data, assigning a label to each of them. -# -# add image here showing an example of "generative model" +# +# .. figure:: ../_static/demonstration_assets/tn_circuits/generative_discriminative.jpg +# :align: center +# :height: 300 # # An important trait of the generative model that allows for this generation of new samples is rooted on its # ability to capture correlations present in the input data. Among the different models employed in the literature @@ -38,9 +40,11 @@ # the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the # training data, this making them suitable candidates be employed in the generative model. -# -# add tensor network image with psi as label both for MPS and TTN. -# +# +# .. figure:: ../_static/demonstration_assets/tn_circuits/tensor_network_wavefunction.jpg +# :align: center +# :height: 300 +# # Tensor networks and Quantum Circuits # ----------------------- # As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wavefunction @@ -63,11 +67,13 @@ # To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a # vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. # -# add drawing of circuit. +# .. figure:: ../_static/demonstration_assets/tn_circuits/quantum_circuit.jpg +# :align: center +# :height: 300 # # Then, we can look at the probability of finding the output wave function in the computational basis state # :math:`\ket{\mathrb{x}}` expressed as -# +# # .. math:: # P_\theta(\mathrb{x}) = \norm*{ \bra{\mathrb{x}}\ket{\psi(\theta)}}^2 # From 72cb195472bbb6e61bb3c257c917bb7249967e82 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Thu, 9 May 2024 18:10:50 -0400 Subject: [PATCH 06/31] solve merge conflicts, erase extra information --- demonstrations/tutorial_qcbm.py | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index 9f69cd9aac..c3d1c57542 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -23,7 +23,7 @@ # to other statistical models like the discriminative model, which allows us to "tell apart" the different instances # present in the the input data, assigning a label to each of them. # -# .. figure:: ../_static/demonstration_assets/tn_circuits/generative_discriminative.jpg +# .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/generative_discriminative.jpg # :align: center # :height: 300 # @@ -41,7 +41,7 @@ # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the # training data, this making them suitable candidates be employed in the generative model. # -# .. figure:: ../_static/demonstration_assets/tn_circuits/tensor_network_wavefunction.jpg +# .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/tensor_network_wavefunction.jpg # :align: center # :height: 300 # @@ -63,11 +63,18 @@ # # .. math:: # \mathrb{x} := (x_1, x_2, \ldots, x_N) \leftrightarrow \ket{\mathrb{x}} := \ket{x_1, x_2, \ldots, x_N} +<<<<<<< HEAD # # To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a # vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. # # .. figure:: ../_static/demonstration_assets/tn_circuits/quantum_circuit.jpg +======= +# +# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. +# +# .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/quantum_circuit.jpg +>>>>>>> f4ece84 (erase extra information) # :align: center # :height: 300 # @@ -316,10 +323,3 @@ def cost_fn_ttn(weights, idxs, true_probs): # Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. Zhang, # *Physical Review X* **8**, 3 (2018), ISSN 2160-3308, # URL ``__ - - -# I can then explain what are generative models generally, how born machine is one model possible, -# and how this has been attempted by using tensor networks. On the other hand it has also been -# attempted with quantum circuits, and here we combine both methods. I can say "quantum circuits are -# a particular instance of tensor networks, and therefore there is a natural connection" -# (cite the diagrammatic representation) From 23b492a031964b1e03581fb2e358d67df0558701 Mon Sep 17 00:00:00 2001 From: EmilianoG-byte Date: Thu, 9 May 2024 18:21:38 -0400 Subject: [PATCH 07/31] fix image path in qcbm --- demonstrations/tutorial_qcbm.py | 7 ------- 1 file changed, 7 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index c3d1c57542..a04df823b2 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -63,18 +63,11 @@ # # .. math:: # \mathrb{x} := (x_1, x_2, \ldots, x_N) \leftrightarrow \ket{\mathrb{x}} := \ket{x_1, x_2, \ldots, x_N} -<<<<<<< HEAD # # To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a # vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. # -# .. figure:: ../_static/demonstration_assets/tn_circuits/quantum_circuit.jpg -======= -# -# To approximate the target distribution, we can create an ansatz for the quantum circuit parametrized by a vector :math:`\theta`, such that the output state vector is defined as :math:`\ket{\psi(\theta)} = U(\theta) \ket{0}`. -# # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/quantum_circuit.jpg ->>>>>>> f4ece84 (erase extra information) # :align: center # :height: 300 # From 090dce58da5d2a27ac79ab97e991e8ce00724913 Mon Sep 17 00:00:00 2001 From: Shiro-Raven Date: Thu, 9 May 2024 19:56:54 -0400 Subject: [PATCH 08/31] Fix formatting of the code section --- demonstrations/tutorial_qcbm.py | 54 +++++++++++++++++++-------------- 1 file changed, 32 insertions(+), 22 deletions(-) diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py index a04df823b2..5c764e23a3 100644 --- a/demonstrations/tutorial_qcbm.py +++ b/demonstrations/tutorial_qcbm.py @@ -12,7 +12,7 @@ *Author: Ahmed Darwish and Emiliano Godinez — Posted: 08 May 2024. Last updated: 08 May 2024.* -In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by `Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. +In this tutorial we employ the NISQ-friendly generative model known as the Quantum Circuit Born Machine (QCBM) introduced by Benedetti, Garcia-Pintos, Perdomo, Leyton-Ortega, Nam and Perdomo-Ortiz (2019) in [#Benedetti]_. to obtain the probability distribution of the bars and stripes data set. To this end, we use the tensor-network inspired templates available in Pennylane to construct the model's ansatz. """ ############################################################################## @@ -22,7 +22,7 @@ # new data instances that follow the probability distribution of the input training data. This is in contrast # to other statistical models like the discriminative model, which allows us to "tell apart" the different instances # present in the the input data, assigning a label to each of them. -# +# # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/generative_discriminative.jpg # :align: center # :height: 300 @@ -40,11 +40,11 @@ # the wave function in terms of tensor networks classes. In particular, the ubiqutious class of Matrix Product # States (MPS) and Tree Tensor Networks (TTN) are capable of capturing the local correlations present in the # training data, this making them suitable candidates be employed in the generative model. -# +# # .. figure:: ../_static/demonstration_assets/qcbm_tensor_network/tensor_network_wavefunction.jpg # :align: center # :height: 300 -# +# # Tensor networks and Quantum Circuits # ----------------------- # As part of the generative model pipeline, it is necessary to draw finite samples from the resulting wavefunction @@ -73,7 +73,7 @@ # # Then, we can look at the probability of finding the output wave function in the computational basis state # :math:`\ket{\mathrb{x}}` expressed as -# +# # .. math:: # P_\theta(\mathrb{x}) = \norm*{ \bra{\mathrb{x}}\ket{\psi(\theta)}}^2 # @@ -87,7 +87,7 @@ # where :math:`C` is the cost function to be optimized, which can take different forms based on the specific # scenario, with the common denominator being that all of them should quantify the difference between the target # probability and the probability distribution obtained from the quantum circuit. Due to the nature of the finite -# sampling used to estimate the distribution, analogous to what is done in classsical generative machine +# sampling used to estimate the distribution, analogous to what is done in classsical generative machine # learning [#Goodfellow]_, in this tutorial we choose the cost function to be the Kullback-Leibler (KL) divergence. # # :math:: @@ -101,7 +101,7 @@ # approaches to generative modelling using tensor networks to represent the wave function, as done in [#Han]_ # and [#Cheng]_ employing MPS and TTN, respectively. Since quantum circuits are a restricted class of tensor # networks, there is a natural relation between them that we can exploit to define a tensor-network inspired ansatz. -# In particular, we take into consideration the local correlations of the data, and employ the MPS and +# In particular, we take into consideration the local correlations of the data, and employ the MPS and # TTN circuit ansatz implemented in Pennylane. See this tutorial `this tutorial `_ # for a deeper study of these ansätze. # @@ -122,10 +122,11 @@ import pennylane as qml from pennylane import numpy as np from qml_benchmarks.data.bars_and_stripes import generate_bars_and_stripes -from tqdm import tqdm import matplotlib.pyplot as plt +############################################################################## # We then configure our random seed and setup some global variables that we will need for our experiments + np.random.seed(1) dev = qml.device("default.qubit", wires=16) @@ -137,6 +138,7 @@ TTN_DATA_SHAPE = (2 ** int(np.log2(QUBITS / 2)) * 2 - 1, 6) +############################################################################## # For generating our dataset, which in our case is the Bar and Stripes dataset, we declare the following function: def prepare_dataset(size, rows, cols): X, _ = generate_bars_and_stripes(size, rows, cols, noise_std=0.0) @@ -161,6 +163,7 @@ def prepare_dataset(size, rows, cols): return idxs, true_probs / size +############################################################################## # Note that for this demo, we assume that the underlying true probability of the dataset # (which is a uniform probability for all elements) is unknown. Rather, we calculate an empirical probability from # the samples generated by the `generate_bars_and_stripes` function. @@ -206,6 +209,7 @@ def qcbm_circuit_ttn(template_weights): return qml.probs() +############################################################################## # You will notice that we do not need to embed any data into the circuit, since QCBMs are generative model! # Any interaction with our dataset will take place in the cost function. @@ -215,11 +219,13 @@ def kl_div(p, q): return np.sum(q * np.log(q / p)) +############################################################################## # We are now ready to train some circuits! Let's generate our dataset first and prepare the optimizer. idxs, true_probs = prepare_dataset(DATASET_SIZE, 4, 4) optimizer = qml.AdamOptimizer() +############################################################################## # Let's start with the MPS circuit: def cost_fn_mps(weights, idxs, true_probs): probs = qcbm_circuit_mps(weights) @@ -231,7 +237,7 @@ def cost_fn_mps(weights, idxs, true_probs): mps_weights = mps_weights_init mps_costs = [] -for it in (pbar := tqdm(range(TRAINING_ITERATIONS))): +for it in range(TRAINING_ITERATIONS + 1): mps_weights = optimizer.step( cost_fn_mps, mps_weights, idxs=idxs, true_probs=true_probs ) @@ -240,8 +246,10 @@ def cost_fn_mps(weights, idxs, true_probs): mps_costs.append(current_cost) - pbar.set_postfix_str(f"KL Loss: {current_cost:.3f}") + if it % 10 == 0: + print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") +############################################################################## # Now we do the same for the TTN network, resetting the optimizer first. optimizer.reset() @@ -256,7 +264,7 @@ def cost_fn_ttn(weights, idxs, true_probs): ttn_weights = ttn_weights_init ttn_costs = [] -for it in (pbar := tqdm(range(TRAINING_ITERATIONS))): +for it in range(TRAINING_ITERATIONS + 1): ttn_weights = optimizer.step( cost_fn_ttn, ttn_weights, idxs=idxs, true_probs=true_probs ) @@ -265,53 +273,55 @@ def cost_fn_ttn(weights, idxs, true_probs): ttn_costs.append(current_cost) - pbar.set_postfix_str(f"KL Loss: {current_cost:.3f}") + if it % 10 == 0: + print(f"Iter: {it:4d} | KL Loss: {current_cost:0.7f}") +############################################################################## # Let's now plot the loss curves of the experiments against each other -plt.plot(range(TRAINING_ITERATIONS), mps_costs, ".b", label="MPS Losses") -plt.plot(range(TRAINING_ITERATIONS), ttn_costs, ".g", label="TTN Losses") +plt.plot(range(TRAINING_ITERATIONS + 1), mps_costs, ".b", label="MPS Losses") +plt.plot(range(TRAINING_ITERATIONS + 1), ttn_costs, ".g", label="TTN Losses") plt.xlabel("Iteration #", fontsize=16) plt.ylabel("KL Loss", fontsize=16) plt.legend() plt.show() -# +############################################################################## # References # ^^^^^^^^^^ # # .. [#Benedetti] # M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, -# *npj Quantum Information* **5**, 1 (2019), ISSN 2056-6387, -# URL ``__ +# "A generative modeling approach for benchmarking and training shallow quantum circuits", +# npj Quantum Information, 2019 # # .. [#Cheng] # S. Cheng, L. Wang, T. Xiang, and P. Zhang, # *Physical Review B* **99**, 15 (2019), ISSN 2469-9969, # URL ``__ - +# # .. [#Ferris] # A. J. Ferris and G. Vidal, # *Physical Review B* **85**, 16 (2012), ISSN 1550-235X, # URL ``__ - +# # .. [#Ballarin] # M. Ballarin, P. Silvi, S. Montangero, and D. Jaschke, # "Optimal sampling of tensor networks targeting wave function's fast decaying tails," (2024), # arXiv:2401.10330 [quant-ph], # URL ``__ - +# # .. [#Harrow] # A. W. Harrow and A. Montanaro, # *Nature* **549**, 7671, 203–209 (2017), ISSN 1476-4687, # URL ``__ - +# # .. [#Goodfellow] # I. Goodfellow, Y. Bengio, and A. Courville, # *Deep Learning* (2016), # MIT Press, # URL ``__ - +# # .. [#Han] # Z.-Y. Han, J. Wang, H. Fan, L. Wang, and P. 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