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  • Open Access

Decoding across Transversal Clifford Gates in the Surface Code

Marc Serra-Peralta1,2,*,†, Mackenzie H. Shaw1,2,*, and Barbara M. Terhal1,2

  • *These authors contributed equally to this work.
  • †Contact author: m.serraperalta@tudelft.nl
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PRX Quantum 7, 010335 – Published 19 February, 2026

DOI: https://doi.org/10.1103/sk5y-25b1

Abstract

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding across logical gates, complicating the decoding task. We show how one can decode across an arbitrary sequence of transversal gates for the unrotated surface code, using a fast “logical observable” minimum-weight perfect matching-based decoder, and benchmark its performance in Clifford circuits under circuit-level noise. We propose windowed logical observable matching decoders to address the problem of fully efficient decoding: our basic windowed decoder is computationally efficient under the restriction of quiescent (slow) resets. Our “advanced” two-step windowed decoder can be computationally inefficient but allows fast resets. For both windowed decoders we identify errors which scale sublinearly in d—depending on the structure of the circuit—which can lead to logical failure, and we propose methods to adapt the decoding to remove such failures. Our work highlights the complexity and interest in efficient decoding of fast logic for the surface code.

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Popular Summary

Quantum error correction (QEC) is believed to be essential for large-scale universal quantum computation. Transversal gates are an attractive way of implementing fault-tolerant gates in mobile-qubit platforms, such as neutral atoms and trapped ions because they are fast, inherently low noise, and allow for fast logic, that is: they can be interspersed with a constant number of QEC cycles. However, classically inferring the errors that have occurred (known as the decoding problem) becomes a more complex task. In particular, standard fast algorithms used for the surface code, a common QEC code, no longer work in the presence of transversal gates. In this paper, we develop a fast and efficient algorithm to decode fast-logic transversal gates in the surface code.

The key insight comes from what we call the “observing region” of a logical observable, which is the region of the quantum circuit in which errors affect the value of the observable. We show that, when solely focusing on the observing region, the decoding problem gets simplified, allowing the use of existing fast algorithms for the surface code to decode observables. This new algorithm strategy is fault-tolerant for universal quantum computation and our numerical simulations show that it achieves high accuracy. We also analyze an adaptation of the proposed method that is computationally efficient, referred to as windowed decoding.

There are still open questions about whether it is possible and how to adapt the proposed method for windowed decoding so that it is both efficient and fault-tolerant.

Article Text

Supplemental Material

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PRX Quantum 7, 010335– Published 19 February, 2026
  • Received 6 June 2025
  • Revised 14 October 2025
  • Accepted 4 December 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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