韩国三星电子公司Gwangsu Yoo团队研究了镜像和占用数反演对称系统变分量子本征求解器的对称性保护变换。该研究于2025年3月19日发表在《物理评论A》杂志上。

变分量子本征求解器（VQE）被认为是近期噪声中尺度量子器件最强大的替代方法之一。然而，VQE的成功实施是相当具有挑战性的，因为ansatz必须具有足够的表达能力，然而，如果它过于表达，可能会阻碍VQE在寻找全局最小值时的优化过程。为了应对VQE的这一挑战，一种常用的方法是应用系统的对称性，这降低了VQE参数空间的维数。

研究组提出了一种可用于具有镜像对称性和占用数反转对称性的系统的量子电路。通过将其应用于寻找安德森杂质模型的本征能量来证明其有用性，安德森杂质模型是各种量子模拟的代表性基本模型。此外，研究组通过将量子电路应用于格林函数的量子算法来证明其可用性，格林函数在理解凝聚态物理的量子系统中起着至关重要的作用。

附：英文原文

Title: Symmetry-protecting ansatz for the variational quantum eigensolver of mirror- and occupation-number-inversion-symmetrical systems

Author: Gwangsu Yoo, Jaehyun Bae, Dae Sin Kim

Issue&Volume: 2025/03/19

Abstract: The variational quantum eigensolver (VQE) is considered one of the most powerful alternative approaches for near-term noisy intermediate-scale quantum devices. However, the successful implementation of the VQE is quite challenging, as the ansatz must be sufficiently expressive, yet, if it is overly expressive, it may hinder the optimization process of the VQE in finding the global minimum. To address this challenge of the VQE, a commonly used approach is to apply the symmetries of the system, which reduces the dimensionality of the parameter space for the VQE. Here, we propose a quantum circuit that can be used for systems with mirror symmetry and occupation-number-inversion symmetry. We demonstrate its usefulness by applying it to find the eigenenergies of the Anderson impurity model, a representative fundamental model for various quantum simulations. In addition, we demonstrate the usability of our quantum circuit by applying it to a quantum algorithm for Green's function, which plays a crucial role in understanding quantum systems of condensed matter physics.

DOI: 10.1103/PhysRevA.111.032615

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.032615