Quantum Monte Carlo simulations

Abstract

Quantum Monte Carlo (QMC) methods offer a powerful suite of computational techniques for tackling quantum many-body problems that are intractable for classical algorithms. By exploiting quantum phenomena such as superposition and entanglement, QMC approaches—particularly those enhanced by quantum algorithms—provide notable improvements in both efficiency and accuracy. This chapter introduces the foundational principles of QMC. It explores recent advancements, including Quantum Amplitude Estimation (QAE), Variational Quantum Monte Carlo (VQMC), and Diffusion Quantum Monte Carlo (DQMC), as well as their integration with quantum walk algorithms. Practical applications are highlighted in areas such as radiation therapy, financial portfolio optimization, and biological system modeling, where Quantum walk-based simulations demonstrate exceptional capability in modeling photon transport, optimizing constrained portfolios, and simulating complex biological dynamics. The chapter concludes by emphasizing the growing convergence of quantum computing and Monte Carlo techniques, forecasting a new era of interdisciplinary breakthroughs in computational science and engineering.