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  • Open Access

Sub-Bath Cooling in Bosonic Systems: Gaussian Constraints and Non-Gaussian Enhancements

Wen-Han Png1, Xueyuan Hu2,*, and Valerio Scarani1,3,†

  • *Contact author: xyhu@sdu.edu.cn
  • †Contact author: physv@nus.edu.sg
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PRX Quantum 7, 020316 – Published 27 April, 2026

DOI: https://doi.org/10.1103/3qnz-6bcz

Abstract

Cooling quantum systems with finite resources is a central task in quantum technologies and has been extensively explored in discrete-variable settings. As continuous-variable (CV) platforms play an increasingly important role in quantum information processing, it becomes crucial to understand the fundamental limitations of cooling bosonic systems. In this work, we develop a general framework for cooling CV systems, identifying both the constraints imposed by Gaussianity and the advantages enabled by non-Gaussian interactions. We derive a reachable bound on the cooling performance of Gaussian operations that applies to arbitrary cooling architectures. By optimizing over all protocols saturating this bound, we further identify the most efficient scheme, which minimizes dissipated energy for a given number of ancilla modes. Beyond Gaussian operations, we show that p-excitation exchange exploits non-Gaussian resources to achieve a p-fold enhancement of the cooling limit. Our results establish the fundamental limits of CV heat-bath algorithmic cooling and reveal the crucial role of non-Gaussianity in surpassing Gaussian cooling barriers.

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Popular Summary

Refrigeration removes heat from a cold system to a hotter one using external work, a process that not only keeps food fresh but also prepares quantum devices in their lowest-energy states. A central challenge in cooling a quantum system is sub-bath cooling: how far a system can be cooled below its environment with minimal energy.

We address this for a quantum harmonic oscillator using multimode Gaussian operations, fully characterizing when sub-bath cooling is possible and determining the optimal Gaussian strategy. The most energy-efficient protocol consists of sequential swaps with auxiliary systems of increasing frequencies, with the frequencies optimized to minimize heat dissipation. We then go beyond Gaussian operations by introducing a non-Gaussian process that exchanges p excitations at a time, achieving a p-fold improvement in cooling performance.

Together, our results establish the ultimate cooling capabilities of Gaussian operations under finite energy and time constraints. We further identify a distinct performance boost enabled by non-Gaussian interactions, which leverage increased control complexity. These findings provide guidance for initializing future quantum bosonic devices.

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Outline

Information

PRX Quantum 7, 020316– Published 27 April, 2026
  • Received 18 December 2025
  • Revised 14 February 2026
  • Accepted 27 March 2026
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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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