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  • Open Access

Cooling a Qubit Using n Others

Jake Xuereb1,*, Benjamin Stratton2,3,†, Alberto Rolandi1, Jinming He4, Marcus Huber1,5, and Pharnam Bakhshinezhad1

  • *Contact author: jake.xuereb@tuwien.ac.at
  • †Contact author: ben.stratton@bristol.ac.uk
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PRX Quantum 6, 040368 – Published 19 December, 2025

DOI: https://doi.org/10.1103/hrph-dbv7

Abstract

In the task of unitarily cooling a quantum system with access to a larger quantum system, known as the machine or reservoir, how does the structure of the machine impact an agent’s ability to cool and the complexity of their cooling protocol? Focusing on the task of cooling a single qubit given access to n separable, thermal qubits with arbitrary energy structure, we answer these questions by giving two new perspectives on this task. First, we show that a set of inequalities related to the energetic structure of the n-qubit machine determines the protocol which cools the qubit to the coldest reachable state, which parts of the machine contribute to this protocol and give rise to a Carnot-like bound. Second, we show that cooling protocols can be represented as perfect matchings on bipartite graphs enabling the optimization of cost functions, e.g., gate complexity or dissipation. Our results generalize the algorithmic cooling problem, establish new fundamental bounds on quantum cooling and offer a framework for designing novel autonomous thermal machines and cooling algorithms.

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Popular Summary

To cool a glass of water we place ice cubes in it, while cooling computer chips requires the use of intricately engineered heat sinks. Ice cubes and heat sinks differ in structure as well as in their cooling properties. In this work, we investigate cooling a qubit with access to other qubits acting as a reservoir and explore how the energetic structure of these reservoir qubits impacts the cooling scenario.

It is a part of the folklore of quantum thermodynamics that cooling a quantum system with access to a reservoir boils down to sorting energy values. But when is this sorting easy and when is it hard? In this work we investigate the structure of this sorting and find that it is “hard” in the sense that it involves many of the reservoir qubits when the energetic structure of the reservoir is a flat landscape. When the energetic landscape is more complex the interaction becomes simple, at times even involving only a single qubit in the reservoir and the system.

We show that this intricate sorting procedure is dictated by simple macroscopic quantities: the temperature of the system, the temperature of the reservoir, and the sum of the energetic gaps of the reservoir qubits. Our insights will allow for the design of more efficient quantum thermodynamic devices that are potentially even capable of error correction.

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Outline

Information

PRX Quantum 6, 040368– Published 19 December, 2025
  • Received 4 July 2025
  • Revised 1 October 2025
  • Accepted 29 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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