Quantum-assisted variational Monte Carlo
arXiv:2502.20799 · doi:10.1021/prechem.5c00025
Abstract
Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced Markov chain Monte Carlo (QeMCMC) algorithm [Nature, 619, 282-287 (2023)], which was originally designed for sampling the Boltzmann distribution of classical spin models using quantum computers, we introduce a quantum-assisted variational Monte Carlo (QA-VMC) algorithm for solving the ground state of quantum many-body systems by adapting QeMCMC to sample the distribution of a (neural-network) wave function in VMC. The central question is whether such quantum-assisted proposal can potentially offer a computational advantage over classical methods. Through numerical investigations for the Fermi-Hubbard model and molecular systems, we demonstrate that the quantum-assisted proposal exhibits larger absolute spectral gaps and reduced autocorrelation times compared to conventional classical proposals, leading to more efficient sampling and faster convergence to the ground state in VMC as well as more accurate and precise estimation of physical observables. This advantage is especially pronounced for specific parameter ranges, where the ground-state configurations are more concentrated in some configurations separated by large Hamming distances. Our results underscore the potential of quantum-assisted algorithms to enhance classical variational methods for solving the ground state of quantum many-body systems.
37 pages, 11 figures
References in corpus (22)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Strong quantum computational advantage using a superconducting quantum processor
- The Hubbard Model
- Emerging quantum computing algorithms for quantum chemistry
- Quantum Simulations of Classical Annealing Processes
- Ab-initio quantum chemistry with neural-network wavefunctions
- Speed-up via Quantum Sampling
- Transformer variational wave functions for frustrated quantum spin systems
- Quantum-enhanced Markov chain Monte Carlo
- Preparing thermal states of quantum systems by dimension reduction
- Single-ancilla ground state preparation via Lindbladians
- Thermal State Preparation via Rounding Promises
- From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
- Quantum Sampling Algorithms for Near-Term Devices
- Simpler (classical) and faster (quantum) algorithms for Gibbs partition functions
- Variational optimization of the amplitude of neural-network quantum many-body ground states
- Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity
- Quantum Dynamical Hamiltonian Monte Carlo
- QAOA-MC: Markov chain Monte Carlo enhanced by Quantum Alternating Operator Ansatz
- From quantum-enhanced to quantum-inspired Monte Carlo
- Quantum-enhanced Markov Chain Monte Carlo for systems larger than your Quantum Computer
- Quantum-assisted variational Monte Carlo