Saturable Quantum Speed Limits for Imaginary-Time Evolution

2025/08/14 by Kobayashi, Kohei
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.10361

Abstract

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= O(log N) within our QSL framework.

Citations

• Quadratic acceleration of multi-step probabilistic algorithms for state preparation
• Simulating non-unitary dynamics using quantum signal processing with unitary block encoding
• A Probabilistic Imaginary Time Evolution Algorithm Based on Non-unitary Quantum Circuit
• Practical Quantum Computation of Chemical and Nuclear Energy Levels Using Quantum Imaginary Time Evolution and Lanczos Algorithms
• Ultimate physical limits to computation
• The maximum speed of dynamical evolution

Related

• A useful fundamental speed limit for the imaginary-time Schrodinger equation
• Attainable quantum speed limit for N-dimensional quantum systems
• Quantum Speed Limits for General Physical Processes
• Family of attainable geometric quantum speed limits
• Quantum-imaginarity-based quantum speed limit