Quantum computing for chemistry and physics applications from a Monte Carlo perspective

Abstract

This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions in quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas in utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.

arXiv comment18 pages, 3 figures. Added new references, fixed some typos

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Cited by in corpus (19)

• Challenges of variational quantum optimization with measurement shot noise
• Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Quantum algorithms for scientific computing
• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
• Quantum Dynamical Hamiltonian Monte Carlo
• A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics
• Quantum computing for genomics: conceptual challenges and practical perspectives
• From quantum-enhanced to quantum-inspired Monte Carlo
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Computing Canonical Averages with Quantum and Classical Optimizers: Thermodynamic Reweighting for QUBO Models of Physical Systems
• Exponential distillation of dominant eigenproperties
• Rovibrational energy levels of H${}_2$O by quantum computing
• Feasibility of performing quantum chemistry calculations on quantum computers
• Quantum Speedup for Nonreversible Markov Chains
• The Quantum Ensemble Variational Optimization Algorithm: Applications to Molecular Inverse Design
• Variational decision diagrams for quantum-inspired machine learning applications