Quantum annealing enhanced Markov-Chain Monte Carlo

Area of Science:

• Computational Physics
• Quantum Computing
• Statistical Mechanics

Background:

• Markov Chain Monte Carlo (MCMC) methods are widely used for sampling complex probability distributions.
• Classical MCMC can struggle with local minima and slow convergence in high-dimensional or complex systems.
• Quantum Annealing (QA) offers a potential pathway to overcome these limitations by efficiently exploring energy landscapes.

Purpose of the Study:

• To introduce and evaluate a hybrid quantum-classical algorithm, Quantum Annealing-Enhanced Markov Chain Monte Carlo (QAEMCMC).
• To assess the performance of QAEMCMC against traditional MCMC methods.
• To demonstrate the potential of QA for accelerating sampling and improving accuracy in complex systems.

Main Methods:

• Integration of Quantum Annealing (QA) into the MCMC sampling subroutine.
• Utilizing QA to explore low-energy configurations and escape local minima.
• Benchmarking QAEMCMC on the Sherrington-Kirkpatrick model.

Main Results:

• QAEMCMC demonstrated superior performance compared to classical MCMC.
• Observed larger spectral gaps, indicating improved exploration of the state space.
• Achieved faster convergence of energy observables and reduced total variation distance.

Conclusions:

• QAEMCMC effectively accelerates MCMC sampling.
• The hybrid approach provides an efficient method for analyzing complex systems.
• This work paves the way for scalable quantum-assisted sampling strategies.