Related papers: Saturable Quantum Speed Limits for Imaginary-Time Evolution

Saturable Quantum Speed Limits for Imaginary-Time Evolution

URL: http://arxiv.org/abs/2508.10361v1
Date: Thu, 14 Aug 2025 05:59:30 GMT
Title: Saturable Quantum Speed Limits for Imaginary-Time Evolution
Authors: Kohei Kobayashi,
Abstract summary: We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution.<n>We analytically evaluate this bound for two physically motivated cases.<n>We rigorously reproduce the well-known logarithmic scaling $T=mathcal O(log N)$ within our framework.
Score: 0.0
License: http://creativecommons.org/licenses/by-sa/4.0/
Abstract: We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a non-unitary Schr\"{o}dinger 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.

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