Grover's search meets Ising models: A quantum algorithm for finding low-energy states

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-04-23 DOI:10.1016/j.cpc.2025.109627

A.A. Zhukov , A.V. Lebedev , W.V. Pogosov

引用次数: 0

Abstract

We propose a methodology for implementing Grover's algorithm in the digital quantum simulation of disordered Ising models. The core concept revolves around using the evolution operator for the Ising model as the quantum oracle within Grover's search. This operator induces phase shifts for the eigenstates of the Ising Hamiltonian, with the most pronounced shifts occurring for the lowest and highest energy states. Determining these states for a disordered Ising Hamiltonian using classical methods presents an exponentially complex challenge with respect to the number of spins (or qubits) involved. Within our proposed approach, we determine the optimal evolution time by ensuring a phase flip for the target states. This method yields a quadratic speedup compared to classical computation methods and enables the identification of the lowest and highest energy states (or neighboring states) with a high probability ≲1.

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Grover的搜索符合Ising模型：一种寻找低能态的量子算法

我们提出了一种在无序Ising模型的数字量子模拟中实现Grover算法的方法。核心概念围绕着使用伊辛模型的演化算子作为格罗弗搜索中的量子预言。这个算子引起了伊辛哈密顿函数特征态的相移，其中最明显的移发生在最低和最高的能量态。使用经典方法确定无序伊辛哈密顿量的这些状态，涉及到自旋（或量子位）的数量，这是一个指数复杂的挑战。在我们提出的方法中，我们通过确保目标状态的相位翻转来确定最优进化时间。与传统的计算方法相比，该方法的速度提高了2倍，并且能够以高概率≤1的方式识别出最低和最高的能态（或相邻态）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.