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  • Open Access

Thermal state preparation by repeated interactions at and beyond the Lindblad limit

Carlos Ramon-Escandell1,*, Alessandro Prositto1, and Dvira Segal1,2,†

  • 1Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
  • 2Department of Chemistry, University of Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6, Canada

  • *Contact author: carlos.ramonescandell@mail.utoronto.ca
  • †Contact author: dvira.segal@utoronto.ca
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Phys. Rev. Research 7, 043012 – Published 2 October, 2025

DOI: https://doi.org/10.1103/5y2q-jzgx

Abstract

We study the nature of thermalization dynamics and the associated preparation (simulation) time under the repeated interaction protocol uncovering an anomalous, Mpemba-like trend. As a case study, we focus on a three-level system and analyze its dynamics in two complementary regimes, where the system-ancilla interaction strength is either large or small. Focusing on the estimation of the simulation time, we derive closed-form expressions for the minimum number of collisions, or minimal simulation time, required to achieve a thermal state, which is within ε distance to the target thermal state. At zero temperature, we analytically identify a set of points (interaction strength × their duration) that minimize the simulation time. At nonzero temperature, we observe a Mpemba-like effect: Starting from a maximally mixed state, thermalization to an intermediate-temperature state takes longer than to a lower-temperature one. We provide an accurate analytical approximation for this phenomenon and demonstrate its occurrence in larger systems and under randomized interaction strengths. The prevalence of the Mpemba effect in thermal state preparation presents a significant challenge for preparing states in large systems, an open problem calling for new strategies.

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Phys. Rev. Research 7, 043012– Published 2 October, 2025
  • Received 13 June 2025
  • Accepted 9 September 2025
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