近日，北京大学袁骁团队研究了量子计算量子蒙特卡罗算法。这一研究成果于2025年8月25日发表在《物理评论A》杂志上。

量子计算（QC）和量子蒙特卡罗（QMC）分别代表了最先进的量子和经典计算方法，用于理解多体量子系统。然而，两种方法的直接集成可能会遇到重大挑战，如指数采样成本和低效的行走者传播。

研究组提出了一种有效的混合量子经典算法，将这两种方法集成在一起，克服了这些限制，同时利用了它们在表示和操纵量子态方面的优势。为了衡量混合方法的有效性，研究组首先引入非稳态指标（NSIs）及其理论上界，这些指标量化了符号问题的严重程度，这是QMC的一个主要限制。接下来，他们提出了一种混合QC-QMC方法，其中行走者由浅量子电路制备的量子态表示。虽然量子态行走者基中的哈密顿量不是稀疏的，但研究组提供了一种有效且可扩展的方法来实现量子计算机的行走者传播。

从QMC的角度来看，他们的算法显著减轻了量子态行走者基中的符号问题。从QC的角度来看，集成QMC增加了浅量子电路的表达能力，使传统上只有更深的量子电路才能实现的更精确的计算成为可能。该方法在处理复杂的量子多体问题上有直接的应用。研究团队对N₂分子（12个量子位）和哈伯德模型（16个量子位）进行了数值测试和验证，观察到符号问题的显著抑制（随着电路深度呈指数下降）和计算精度的显着提高（与变分量子算法相比，这大约是两到三个数量级）。该工作为解决中等规模和早期容错量子计算机的实际问题铺平了道路，在化学、凝聚态物理和材料领域有着广泛的应用。

附：英文原文

Title: Quantum computing quantum Monte Carlo algorithm

Author: Yukun Zhang, Yifei Huang, Jinzhao Sun, Dingshun Lv, Xiao Yuan

Issue&Volume: 2025/08/25

Abstract: Quantum computing (QC) and quantum Monte Carlo (QMC) represent state-of-the-art quantum and classical computing methods, respectively, for understanding many-body quantum systems. However, straightforward integration of the two methods may encounter significant challenges, such as exponential sampling cost and inefficient walker propagation. Here, we propose an efficient hybrid quantum-classical algorithm that integrates the two methods, overcoming these limitations while leveraging their strengths in representing and manipulating quantum states. To measure the effectiveness of the hybrid approach, we first introduce nonstoquasticity indicators (NSIs) and their theoretical upper bounds, which quantify the severity of the sign problem, a major limitation of QMC. Next, we present a hybrid QC-QMC method where the walkers are represented by quantum states prepared by a shallow quantum circuit. Although the Hamiltonian in the quantum state walker basis is not sparse, we offer an efficient and scalable approach to implement walker propagation using a quantum computer. From the QMC perspective, our algorithm significantly mitigates the sign problem in the quantum state walker basis. From the QC perspective, integrating QMC increases the expressivity of shallow quantum circuits, enabling more accurate computations that are traditionally achievable only with much deeper quantum circuits. Our method has immediate applications in tackling complex quantum many-body problems. We numerically test and verify it for the N2 molecule (12 qubits) and the Hubbard model (16 qubits), observing a significant suppression of the sign problem (which exponentially decreases with circuit depth) and a notable improvement in calculation accuracy (which is about two to three orders compared to variational quantum algorithms). Our work paves the way to solving practical problems with intermediate-scale and early fault-tolerant quantum computers, with broad applications in chemistry, condensed matter physics, and materials.

DOI: 10.1103/jt8s-hzhd

Source: https://journals.aps.org/pra/abstract/10.1103/jt8s-hzhd