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  • Open Access

Fault-Tolerant Quantum Computation with Constant Overhead for General Noise

Matthias Christandl1,*, Omar Fawzi2,†, and Ashutosh Goswami1,‡

  • *Contact author: christandl@math.ku.dk
  • †Contact author: omar.fawzi@ens-lyon.fr
  • ‡Contact author: akg@math.ku.dk
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PRX Quantum 6, 040334 – Published 13 November, 2025

DOI: https://doi.org/10.1103/k4cm-pp9p

Abstract

Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman has shown that constant qubit overhead is achievable under stochastic noise using quantum low-density parity-check (QLDPC) codes, it has remained an open question whether similar guarantees hold under more general, nonstochastic noise models. In this work, we address this question by considering a general circuit-level noise model defined via the diamond norm, which captures both stochastic and nonstochastic noise, including coherent and amplitude damping noise. We prove that constant qubit overhead fault-tolerant quantum computation is achievable in this general setting, using QLDPC codes with constant rate and linear minimum distance. To establish our result, we develop a fault-tolerant error correction scheme and a method for implementing logic gates under general circuit noise. These results extend the theoretical foundations of fault-tolerant quantum computation and offer new directions for fault-tolerant architectures under realistic noise models.

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Popular Summary

Quantum computers promise to solve problems that are beyond the reach of today’s machines. However, a major obstacle in building quantum computers is noise, which introduces errors in computation. Left unchecked, these errors can quickly spread and derail the entire computation. To address this, researchers use fault-tolerant quantum computation (FTQC), where errors are actively corrected as the computation runs. However, existing fault-tolerant methods come with a steep price, demanding many more qubits and much longer run-times than the original computation, making FTQC very challenging in practice.

Here, we focus on reducing the qubit overhead, i.e., the ratio of qubits required in the fault-tolerant computation to those in the original. A central question is whether fault tolerance can be achieved with constant qubit overhead, i.e., the number of extra qubits needed remains bounded by a fixed factor, regardless of how large the computation becomes. Previous research has shown that this is possible under simplified noise models, such as Pauli or stochastic noise, where errors behave randomly in the classical sense. However, real quantum devices experience more complex noise, often coherent in nature, which these models cannot capture. Whether constant-overhead fault tolerance remains possible under such general noise has, until now, been unresolved.

In this work, we answer this question positively. We prove that constant-overhead FTQC can be achieved even under a broad and realistic class of noise, including coherent errors. Our results provide rigorous guarantees under realistic noise models, making a step forward in the study of FTQC.

Article Text

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Outline

Information

PRX Quantum 6, 040334– Published 13 November, 2025
  • Received 3 May 2025
  • Revised 8 September 2025
  • Accepted 18 September 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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