Saturable Quantum Speed Limits for Imaginary-Time Evolution
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913991167574016 |
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| author | Kobayashi, Kohei |
| author_facet | Kobayashi, Kohei |
| contents | We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a non-unitary Schrödinger equation. By introducing a cost function based on the angular distance between the normalized evolving state and the initial state, we obtain a lower bound on the evolution time expressed as the ratio between this angle and the time-averaged energy dispersion. Our bound is analytical, general, and applicable to arbitrary time-independent Hamiltonians. We analytically evaluate this bound for two physically motivated cases. First, we apply it to a two-level system and derive an expression for the minimal time. Second, we analyze the imaginary-time version of Grover search problem and rigorously reproduce the well-known logarithmic scaling $T=\mathcal{ O}(\log N)$ within our QSL framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Saturable Quantum Speed Limits for Imaginary-Time Evolution Kobayashi, Kohei Quantum Physics We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a non-unitary Schrödinger equation. By introducing a cost function based on the angular distance between the normalized evolving state and the initial state, we obtain a lower bound on the evolution time expressed as the ratio between this angle and the time-averaged energy dispersion. Our bound is analytical, general, and applicable to arbitrary time-independent Hamiltonians. We analytically evaluate this bound for two physically motivated cases. First, we apply it to a two-level system and derive an expression for the minimal time. Second, we analyze the imaginary-time version of Grover search problem and rigorously reproduce the well-known logarithmic scaling $T=\mathcal{ O}(\log N)$ within our QSL framework. |
| title | Saturable Quantum Speed Limits for Imaginary-Time Evolution |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.10361 |