From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914376836972544 |
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| author | Čindrak, Saud Lüdge, Kathy Jaurigue, Lina |
| author_facet | Čindrak, Saud Lüdge, Kathy Jaurigue, Lina |
| contents | We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in the framework of quantum reservoir computing and show that it closely mirrors information processing capacity, a data-driven expressivity metric, while achieving computation times that are orders of magnitude faster. Our results validate Operator complexity and give the interpretation that data in a quantum reservoir is mapped onto the Krylov space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing Čindrak, Saud Lüdge, Kathy Jaurigue, Lina Quantum Physics We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in the framework of quantum reservoir computing and show that it closely mirrors information processing capacity, a data-driven expressivity metric, while achieving computation times that are orders of magnitude faster. Our results validate Operator complexity and give the interpretation that data in a quantum reservoir is mapped onto the Krylov space. |
| title | From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.12157 |