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  • Open Access

Scalable Decoding Protocols for Fast Transversal Logic in the Surface Code

Mark L. Turner1,*, Earl T. Campbell1,2, Ophelia Crawford1, Neil I. Gillespie1, and Joan Camps1

  • *Contact author: mark.turner@riverlane.com
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PRX Quantum 7, 010320 – Published 29 January, 2026

DOI: https://doi.org/10.1103/nx6p-hjqy

Abstract

Atomic, molecular and optical (AMO) approaches to quantum computing are promising due to their increased connectivity, long coherence times and apparent scalability. However, they have a significantly reduced cadence of syndrome extraction compared to superconducting devices, a potentially crippling slow-down given the substantial logical gate counts required for quantum advantage. Transversal logic, which exploits higher connectivity, has the potential to significantly speed up the logical clock rate by reducing the number of syndrome extraction rounds required, but current decoders for fast transversal logic are not scalable. This is not just because existing decoders are too slow to handle the large decoding volumes resulting from fast logic; transversal logic breaks the key structural properties that make real-time decoding of lattice surgery efficient. We introduce two windowed decoding protocols for transversal logic in the surface code that restore modularity and locality to the decoding problem. Using our protocols, we show that, with a very small space overhead, our scalable decoders unlock an order of magnitude speedup for transversal logic compared to lattice surgery. Taken together, our results provide key evidence for the viability of large-scale algorithms on AMO qubits.

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Popular Summary

Atomic, molecular and optical (AMO) approaches to fault-tolerant quantum computing have many attractive properties, including high-fidelity gates and increased connectivity, but are much slower than their superconducting counterparts. However, their ability to implement logical gates transversally means AMO qubits can compensate for slower physical gates with reduced overhead in logical gates compared to other dominant modes of fault-tolerant logic.

Correcting errors in this circuitry requires classical processing of measurement data from the quantum computer in real time using decoders. Importantly, the complexity introduced by transversal gates results in a more intricate decoding challenge known as a correlated (or hypergraph) decoding problem. A common assumption has been that the inapplicability of existing windowing schemes to fast transversal logic and the growth of the decoding volume in this particular setting makes a transversal speedup difficult to attain in practice.

To address this, we propose two decoding protocols where each logical qubit is decoded independently in an iterative fashion, each time exchanging messages with other decoders looking after other logical qubits. These protocols enable fast, modular and accurate decoding of fast transversal logic important for scalable error correction in AMO quantum computers.

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PRX Quantum 7, 010320– Published 29 January, 2026
  • Received 29 May 2025
  • Revised 9 October 2025
  • Accepted 15 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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