Quantum Dynamics in Krylov Space: Methods and Applications
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911006773477376 |
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| author | Nandy, Pratik Matsoukas-Roubeas, Apollonas S. Martínez-Azcona, Pablo Dymarsky, Anatoly del Campo, Adolfo |
| author_facet | Nandy, Pratik Matsoukas-Roubeas, Apollonas S. Martínez-Azcona, Pablo Dymarsky, Anatoly del Campo, Adolfo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Dynamics in Krylov Space: Methods and Applications Nandy, Pratik Matsoukas-Roubeas, Apollonas S. Martínez-Azcona, Pablo Dymarsky, Anatoly del Campo, Adolfo Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Chaotic Dynamics 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. |
| title | Quantum Dynamics in Krylov Space: Methods and Applications |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2405.09628 |