Quantum Computing Quantum Monte Carlo
Xiao Hui Yuan, Yukun Zhang, Yifei Huang, Jinzhao Sun, Dingshun Lv · Research Square · 2024
Abstract Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, measuring the severity of the sign problem, the most notable limitation of QMC. Then we introduce the hybrid QC-QMC method by replacing the walkers with quantum states prepared by a shallow quantum circuit. We present an efficient and scalable approach to implement walker propagation in QC-QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.