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  • Open Access

Exploring Noisy Quantum Thermodynamical Processes via the Depolarizing-Channel Approximation

Jian Li1,2, Xiaoyang Wang3,4,*, Marcus Huber1,5, Nicolai Friis1, and Pharnam Bakhshinezhad1,†

  • *Contact author: xiaoyang.wang@riken.jp
  • †Contact author: pharnam.bakhshinezhad@tuwien.ac.at
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Phys. Rev. Lett. 137, 190401 – Published 2 November, 2026

DOI: https://doi.org/10.1103/wg2x-z2vm

Abstract

Noise and errors are unavoidable in any realistic quantum process, including processes designed to reduce noise and errors in the first place. In particular, quantum thermodynamical protocols for cooling can be significantly affected, potentially altering both their performance and efficiency. Analytically characterizing the impact of such errors becomes increasingly challenging as the system size grows, particularly in deep quantum circuits where noise can accumulate in complex ways. To address this, we introduce a general framework for approximating the cumulative effect of gate-dependent noise using a global depolarizing channel. We specify the regime in which this approximation provides a reliable description of the noisy dynamics. Applying our framework to the thermodynamical two-sort algorithmic cooling (TSAC) protocol, we analytically derive its asymptotic cooling limit in the presence of noise. Using the cooling limit, the optimal cooling performance is achieved by a finite number of qubits—distinguished from the conventional noiseless TSAC protocol by an infinite number of qubits—and fundamental bounds on the achievable ground-state population are derived. This approach opens new avenues for exploring noisy quantum thermodynamical processes.

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Phys. Rev. Lett. 137, 190401– Published 2 November, 2026
  • Received 13 February 2026
  • Revised 16 June 2026
  • Accepted 8 October 2026
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