Quantum dynamics in Krylov space: Methods and applications

IF 23.9 1区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Physics Reports Pub Date : 2025-05-15 DOI:10.1016/j.physrep.2025.05.001

Pratik Nandy , Apollonas S. Matsoukas-Roubeas , Pablo Martínez-Azcona , Anatoly Dymarsky , Adolfo del Campo

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Abstract

The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and quantum chaos, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems.

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克雷洛夫空间中的量子动力学：方法与应用

量子系统的动力学在状态空间或算符空间的子空间中展开，称为克里洛夫空间。本文介绍了使用Krylov子空间方法来提供量子演化和量子混沌的有效描述，重点介绍了具有大希尔伯特空间的多体系统的非平衡现象。它提供了最近发展的全面更新，重点是海森堡图像中算子的量子演化以及纯态和混合态。它进一步探讨了Krylov复杂度和相关度量作为量化算子增长的工具的概念，它们的广义量子速度极限的界限，通用算子增长假设，以及它与量子混沌，乱置和广义相干态的关系。对开放量子系统的克雷洛夫构造的几种推广进行了比较。最后讨论了Krylov子空间方法在量子场论、全息、可积性、量子控制和量子计算中的应用，以及当前的开放问题。

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

Physics Reports 物理-物理：综合

CiteScore

56.10

自引率

0.70%

发文量

102

审稿时长

9.1 weeks

期刊介绍： Physics Reports keeps the active physicist up-to-date on developments in a wide range of topics by publishing timely reviews which are more extensive than just literature surveys but normally less than a full monograph. Each report deals with one specific subject and is generally published in a separate volume. These reviews are specialist in nature but contain enough introductory material to make the main points intelligible to a non-specialist. The reader will not only be able to distinguish important developments and trends in physics but will also find a sufficient number of references to the original literature.