Properties of Krylov state complexity in qubit dynamics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915248207822848 |
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| author | Seetharaman, Siddharth Singh, Chetanya Nath, Rejish |
| author_facet | Seetharaman, Siddharth Singh, Chetanya Nath, Rejish |
| contents | We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for the two-qubit case. Considering the particular case of interacting Rydberg two-level atoms, we show that the Krylov basis obtained using an effective Hamiltonian minimizes the time-averaged spread complexity compared to that which is obtained from the original Hamiltonian. We further generalize the latter property to an arbitrary Hamiltonian in which the entire Hilbert space comprises of two subspaces provided a weak coupling between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of Krylov state complexity in qubit dynamics Seetharaman, Siddharth Singh, Chetanya Nath, Rejish Quantum Physics Quantum Gases We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for the two-qubit case. Considering the particular case of interacting Rydberg two-level atoms, we show that the Krylov basis obtained using an effective Hamiltonian minimizes the time-averaged spread complexity compared to that which is obtained from the original Hamiltonian. We further generalize the latter property to an arbitrary Hamiltonian in which the entire Hilbert space comprises of two subspaces provided a weak coupling between them. |
| title | Properties of Krylov state complexity in qubit dynamics |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2407.21776 |