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  • Open Access

Neural Decoders for Universal Quantum Algorithms

J. Pablo Bonilla Ataides*,†, Andi Gu*,‡, Susanne F. Yelin§, and Mikhail D. Lukin‖

  • *These authors contributed equally to this work.
  • †Contact author: jbonillaataides@g.harvard.edu
  • ‡Contact author: andigu@g.harvard.edu
  • §Contact author: syelin@g.harvard.edu
  • ‖Contact author: lukin@physics.harvard.edu
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PRX Intelligence 1, 013008 – Published 4 August, 2026

DOI: https://doi.org/10.1103/vjn1-mbxl

Abstract

Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning decoders have demonstrated impressive performance for quantum memory, their use in algorithmic decoding—where logical gates create complex error correlations—remains limited. We introduce a modular attention-based neural decoder that learns gate-induced correlations and generalizes from training on random circuits to unseen multiqubit algorithmic workloads. Our decoders achieve fast inference and logical error rates comparable to most-likely-error decoders across varied circuit depths and qubit counts. Addressing realistic noise, we incorporate loss-resolving readout, yielding substantial gains when qubit loss is present. We further show that by tailoring the decoder to the structure of the algorithm and decoding only the relevant observables, we can simplify the decoder design without sacrificing accuracy. We validate our framework on multiple error correction codes—including surface codes and two-dimensional color codes—and demonstrate state-of-the-art performance under circuit-level noise. Finally, we show that the attention mechanism learns to track physically meaningful error correlations, consistent with the expected propagation pathways through entangling gates. Enabling experimental validation of deep-circuit fault-tolerant algorithms and architectures [Bluvstein et al., Nature (London) 649, 39 (2026)], these results establish neural decoders as practical, versatile, and high-performance tools for quantum computing.

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PRX Intelligence 1, 013008– Published 4 August, 2026
  • Received 10 November 2025
  • Accepted 23 June 2026
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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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