# Hybrid quantum-classical simulation of quantum speed limits in open quantum systems

## TL;DR

This paper introduces a hybrid quantum-classical approach to efficiently compute quantum speed limits in open quantum systems, revealing how coupling strength and temperature influence quantum evolution speed and energy transfer efficiency.

## Contribution

The paper presents a novel mixed Wigner-Heisenberg method for calculating quantum speed limits in multi-level open systems, combining quantum and classical dynamics for improved analysis.

## Key findings

- QSL time exhibits a turnover in strong coupling regimes.
- Subsystem-bath interactions significantly affect quantum evolution speed.
- Potential link between QSL time and energy transfer efficiency in biological systems.

## Abstract

The quantum speed limit (QSL) provides a fundamental upper bound on the speed of quantum evolution, but its evaluation in generic open quantum systems still presents a formidable computational challenge. Herein, we introduce a hybrid quantum-classical method for computing QSL times in multi-level open quantum systems. The method is based on a mixed Wigner-Heisenberg representation of the composite quantum dynamics, in which the open subsystem of interest is treated quantum mechanically and the bath is treated in a classical-like fashion. By solving a set of coupled first-order deterministic differential equations for the quantum and classical degrees of freedom, one can compute the QSL time. To demonstrate the utility of the method, we study the unbiased spin-boson model and provide a detailed analysis of the effect of the subsystem-bath coupling strength and bath temperature on the QSL time. In particular, we find a turnover of the QSL time in the strong coupling regime, which is indicative of a speed-up in the quantum evolution. We also apply the method to the Fenna- Matthews-Olson complex model and identify a potential connection between the QSL time and the efficiency of the excitation energy transfer at different temperatures.