Saturable Quantum Speed Limits for Imaginary-Time Evolution

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1. Verfasser: Kobayashi, Kohei
Format: Preprint
Veröffentlicht: 2025
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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