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  • Open Access

High-Threshold, Low-Overhead and Single-Shot Decodable Fault-Tolerant Quantum Memory

Thomas R. Scruby1,*, Timo Hillmann2,3,†, and Joschka Roffe4,5,‡

  • *Contact author: t.r.scruby@gmail.com
  • †Contact author: timo.hillmann@rwth-aachen.de
  • ‡Contact author: joschka@roffe.eu
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PRX Quantum 7, 020310 – Published 17 April, 2026

DOI: https://doi.org/10.1103/67xf-zdjb

Abstract

We present a family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasicyclic codes. The codes are defined using a pair of integers (r,s) and have parameters ⟦2r2s,2(r−1)2,≤2s⟧, with numerical studies suggesting average-case distance linear in s. In simulations of circuit-level noise, we observe comparable error suppression to surface codes of similar distance while using approximately five times fewer physical qubits. This is true even when radial codes are decoded using a single-shot approach, which can allow for faster logical clock speeds and reduced decoding complexity. We describe an intuitive visual representation, canonical basis of logical operators and optimal-length stabilizer measurement circuits for these codes, and argue that their error correction capabilities, tunable parameters and small size make them promising candidates for implementation on near-term quantum devices.

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Popular Summary

Quantum low-density parity-check codes are a compelling alternative to the surface code for fault-tolerant quantum computation. Beyond improved encoding density, an often overlooked advantage is that some constructions support the single-shot property, which enables more efficient decoding and can reduce the time required to execute logical operations. In this work, we introduce radial codes, a new family specifically designed to exhibit this single-shot behavior. We present several examples at experimentally relevant scales that are competitive with state-of-the-art bivariate bicycle codes. We analyze their confinement properties and verify the single-shot behavior through numerical simulations.

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Outline

Information

PRX Quantum 7, 020310– Published 17 April, 2026
  • Received 27 October 2025
  • Revised 9 February 2026
  • Accepted 6 March 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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