Streamlined Krylov construction and classification of ergodic Floquet systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909609857384448 |
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| author | Kolganov, Nikita Trunin, Dmitrii A. |
| author_facet | Kolganov, Nikita Trunin, Dmitrii A. |
| contents | We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a one-dimensional tight-binding Krylov chain, which is efficiently simulated on both classical and quantum computers. We also suggest a classification of chaotic and integrable Floquet systems based on the asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients). We illustrate this classification with random matrix ensembles, kicked top, and kicked Ising chain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Streamlined Krylov construction and classification of ergodic Floquet systems Kolganov, Nikita Trunin, Dmitrii A. Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Chaotic Dynamics We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a one-dimensional tight-binding Krylov chain, which is efficiently simulated on both classical and quantum computers. We also suggest a classification of chaotic and integrable Floquet systems based on the asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients). We illustrate this classification with random matrix ensembles, kicked top, and kicked Ising chain. |
| title | Streamlined Krylov construction and classification of ergodic Floquet systems |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2412.19797 |