Robustness of the quantum Mpemba effect against state-preparation errors

TL;DR

This paper investigates the robustness of the quantum Mpemba effect under state-preparation errors, comparing models with open system dynamics and symmetric circuits, revealing differing sensitivities to noise.

Contribution

It demonstrates that certain quantum thermalisation models are highly sensitive to initial state errors, while symmetry restoration in circuits is more robust and can even be enhanced by errors.

Findings

Open system thermalisation is highly sensitive to initial state noise.

Symmetry restoration in circuits remains robust despite state errors.

Large errors can accelerate symmetry restoration and strengthen the QME.

Abstract

The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in $U(1)$ symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.