美国加州理工学院Leo Zhou小组的最新研究发现了量子系统中的局部最小值。2025年2月18日出版的《自然—物理学》杂志发表了这项成果。

众所周知，经典计算机和量子计算机都很难找到量子多体系统的基态。因此，当量子系统在低温热浴中冷却时，无法确保有效地找到基态。相反，系统可能会陷入能量的局部最小值。

在这项工作中，研究组分析了在热扰动下量子系统中寻找局部最小值的问题。尽管局部最小值比基态更容易找到，但研究发现，在经典计算机上很难找到局部最小值，即使任务只是在可观察到的任何局部最小值处输出单个量子比特。

相比之下，研究组证明量子计算机总是可以使用模拟自然冷却过程的热梯度下降算法有效地找到局部最小值。为了建立寻找局部最小值的经典难度，他们构造了一个二维哈密顿算子族，使得任何可由多项式时间量子算法解决的问题都可以简化为寻找这些哈密顿算子的局部最小值。因此，将系统冷却到局部最小值对于量子计算来说是普遍的，假设量子计算比经典计算更强大，找到局部最小值在经典上很难，但在量子上很容易实现。

附：英文原文

Title: Local minima in quantum systems

Author: Chen, Chi-Fang, Huang, Hsin-Yuan, Preskill, John, Zhou, Leo

Issue&Volume: 2025-02-18

Abstract: Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. Consequently, when a quantum system is cooled in a low-temperature thermal bath, the ground state cannot always be found efficiently. Instead, the system may become trapped in a local minimum of the energy. In this work, we study the problem of finding local minima in quantum systems under thermal perturbations. Although local minima are much easier to find than ground states, we show that finding a local minimum is hard on classical computers, even when the task is merely to output a single-qubit observable at any local minimum. By contrast, we prove that a quantum computer can always find a local minimum efficiently using a thermal gradient descent algorithm that mimics natural cooling processes. To establish the classical hardness of finding local minima, we construct a family of two-dimensional Hamiltonians such that any problem solvable by polynomial-time quantum algorithms can be reduced to finding local minima of these Hamiltonians. Therefore, cooling systems to local minima is universal for quantum computation and, assuming that quantum computation is more powerful than classical computation, finding local minima is classically hard but quantumly easy.

DOI: 10.1038/s41567-025-02781-4

Source: https://www.nature.com/articles/s41567-025-02781-4