This repository gathers implementations and explorations of Quantum Monte Carlo (QMC) methods, focusing on the theoretical aspects of quantum-enhanced and quantum-inspired algorithms.
The aim is to study how quantum resources — or their classical analogues — can improve sampling, integration, and optimization tasks in physics.
- Quantum-Enhanced Markov Chain Monte Carlo (QeMCMC): exploring accelerated convergence in sampling distributions.
- Quantum-Inspired Monte Carlo: developing classical algorithms informed by quantum methods.
- Quantum-Assisted Variational Monte Carlo (VMC): hybrid approaches combining classical sampling with quantum variational ansätze.
- Scaling studies: analyzing algorithms for systems larger than current quantum computers can handle.
- Ising Models: classical and transverse-field Ising models as testbeds for QMC methods.
- Spin Chains: 1D and 2D spin lattices under quantum and thermal fluctuations.
- Many-Body Physics: Monte Carlo approaches to study correlations, phase transitions, and ground state properties.
- Benchmark Problems: comparing QMC methods against exact diagonalization or tensor-network simulations.
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Quantum-Enhanced Markov Chain Monte Carlo — David Layden et al. (Nature, 2023)
Nature 619, 282–287 (2023) -
From Quantum-Enhanced to Quantum-Inspired Monte Carlo — Johannes Christmann et al. (Phys. Rev. A, 2025)
Phys. Rev. A 111, 042615 (2025) -
Quantum-Enhanced Markov Chain Monte Carlo for Systems Larger Than Your Quantum Computer — Stuart Ferguson & Petros Wallden (arXiv preprint, 2024)
arXiv:2405.04247 (2024) -
Quantum-Assisted Variational Monte Carlo — Longfei Chang et al. (please add DOI/arXiv link if available)
- Quantum frameworks: Qiskit, PennyLane, Cirq
- Numerical libraries: NumPy, SciPy, PyTorch, JAX
- Simulation platforms: classical tensor-network solvers, AWS Braket, IBM Quantum simulators
- Visualization: Matplotlib, Seaborn, Jupyter Notebooks
Quantum Monte Carlo methods sit at the interface of statistical physics, quantum many-body theory, and computational sciences.
Studying transverse-field Ising models and related spin systems provides an ideal playground for testing QMC ideas — revealing how quantum resources may speed up sampling or inspire new classical algorithms.
Contributions are welcome in the form of new implementations, benchmark studies, or extensions to other quantum many-body systems.
Distributed under the MIT License.