Quantum speed limit for complex dynamics

TL;DR

This paper introduces a machine learning-based three-step methodology to accurately evaluate the true quantum speed limit in complex many-body dynamics, surpassing traditional lower-bound approaches.

Contribution

It presents a novel classification-regression-calibration approach for determining the true minimum evolution time in complex quantum systems, including analytical solutions for specific Hamiltonians.

Findings

The method accurately estimates the true quantum speed limit in complex scenarios.

It outperforms traditional lower-bound methods in complex many-body systems.

Analytical expressions are derived for certain time-dependent Hamiltonians.

Abstract

Quantum speed limit focuses on the minimum time scale for a fixed mission and hence is important in quantum information where fast dynamics is usually beneficial. Most existing tools for the depiction of quantum speed limit are the lower-bound-type tools, which are in fact difficult to reveal the true minimum time, especially for many-body systems or complex dynamics. Therefore, the evaluation of this true minimum time in these scenarios is still an unsolved problem. Hereby we propose a three-step (classification-regression-calibration) methodology based on machine learning to evaluate the true minimum time in complex dynamics. Moreover, the analytical expression of the true minimum time is also provided for the time-dependent Hamiltonians with time-independent eigenstates.