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  • Open Access

Complexity of Local Quantum Circuits under Nonunital Noise

Oles Shtanko1,* and Kunal Sharma2,†

  • *Contact author: oles.shtanko@ibm.com
  • †Contact author: kunals@ibm.com
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PRX Quantum 6, 030347 – Published 11 September, 2025

DOI: https://doi.org/10.1103/xwz2-wfr4

Abstract

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless midcircuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as depolarizing noise. Building on the idea of the “quantum refrigerator” Ben-Or et al. [Quantum refrigerator, arXiv1301.1995 (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension d≥1, can correct errors without midcircuit measurements and extend computation to any depth, with only polylogarithmic overhead in the depth and the number of qubits. This implies that local quantum dynamics subjected to sufficiently weak nonunital noise are computationally universal and nearly as hard to simulate as noiseless dynamics. Additionally, we quantify the contraction property of local random circuits in the presence of nonunital noise.

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Popular Summary

The claim that noisy quantum circuits are only suitable for logarithmic depth algorithms is widely accepted, largely because of analyses of depolarizing noise—a type of unital noise that drives the system toward a maximally mixed state. While mathematically convenient, unital noise imposes several limitations. By continually increasing entropy, it makes deep quantum computation infeasible without frequent measurement and feedback.

But what about nonunital noise, such as amplitude damping, which naturally arises in superconducting qubit systems? Surprisingly, even a small degree of nonunital noise can significantly change this narrative. Nonunital noise possesses a “cooling effect” that can be harnessed to enable quantum error correction, extending computation times arbitrarily with only polylogarithmic overhead. This implies that local quantum circuits with sufficiently weak nonunital noise can be computationally universal, making them nearly as challenging to simulate as noiseless systems. This sharply contrasts with the logarithmic depth constraints imposed by unital noise.

Our key contribution is a rigorous proof that this phenomenon holds for geometrically local circuits in any dimension, including two-dimensional architectures such as those employed on state-of-the-art quantum hardware as well as simpler one-dimensional configurations.

Why is our result significant? This result introduces a pathway to design circuits that are inherently resilient to nonunital noise, offering a new direction for noise-mitigation strategies. However, whether such circuits can be efficiently trained or learned remains an open and intriguing question.

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PRX Quantum 6, 030347– Published 11 September, 2025
  • Received 10 January 2025
  • Revised 22 May 2025
  • Accepted 16 July 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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