Dynamical codes for hardware with noisy readouts

Peter-Jan H.S. Derks; Alex Townsend-Teague; Jens Eisert; Markus S. Kesselring; Oscar Higgott; Benjamin J. Brown

doi:10.22331/q-2026-07-29-2176

Dynamical codes for hardware with noisy readouts

Peter-Jan H.S. Derks¹, Alex Townsend-Teague¹, Jens Eisert¹, Markus S. Kesselring¹, Oscar Higgott², and Benjamin J. Brown^3,4

¹Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
²Department of Physics & Astronomy, University College London, WC1E 6BT London, United Kingdom
³IBM Quantum, T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
⁴IBM Denmark, Sundkrogsgade 11, 2100 Copenhagen, Denmark

Published:	2026-07-29, volume 10, page 2176
Editor:	Kishor Bharti
Eprint:	arXiv:2505.07658v2
Doi:	https://doi.org/10.22331/q-2026-07-29-2176
Citation:	Quantum 10, 2176 (2026).

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Abstract

Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how best to optimise the measurement schedule of dynamically condensed colour codes in various limits of noise bias. We take a particular focus on the setting where measurements introduce more noise than unitary and idling operations – a noise model relevant to some hardware proposals. For measurement-biased noise models, we improve code performance by strategically repeating measurements within the schedule. For unbiased or $Z$-biased noise models, we find repeating measurements offers little improvement – somewhat contrary to our expectations – and investigate why this is. To perform this analysis, we generalise a metric called the teraquop footprint to the teraquop volume. This is the product of the number of qubits and number of rounds of measurements required such that the probability of a spacelike or timelike logical error occurring is less than $10^{-12}$. In most cases, we find differences in performance are primarily due to the number of rounds of measurements required, rather than the number of qubits – emphasising the importance of using the teraquop volume in the analysis. Additionally, our results provide another example of the importance of making use of correlated errors when decoding, in that using belief matching rather than minimum-weight perfect matching can turn a worst-performing code under a given noise model into a best-performing code.

Popular summary

Large-scale quantum computers will need to protect fragile quantum information from errors. A leading approach is quantum error correction, in which errors are detected by repeatedly measuring carefully chosen properties of the quantum system. Surprisingly, not only what is measured matters, but also when and in what order these measurements are performed.

In this work, we study a family of quantum error-correcting codes known as dynamical stabilizer codes, where the measurement schedule itself becomes part of the code design. We investigate how these schedules should be optimized for different hardware platforms, with a particular focus on devices where quantum measurements are significantly noisier than other operations. We find that repeating selected measurements can substantially improve performance when measurement errors dominate, while providing little benefit when other error sources are equally important.

To compare different measurement schedules, we introduce the teraquop volume, a metric that combines both the number of physical qubits and the time required to suppress logical errors below a practically relevant threshold of $10^{-12}$. Using this metric, we show that both the measurement schedule and the decoding algorithm can dramatically affect the resources required for fault-tolerant quantum computation. Our results provide practical guidance for tailoring quantum error-correcting codes to the strengths and weaknesses of future quantum computing hardware.

► BibTeX data

@article{Derks2026dynamicalcodes,
  doi = {10.22331/q-2026-07-29-2176},
  url = {https://doi.org/10.22331/q-2026-07-29-2176},
  title = {Dynamical codes for hardware with noisy readouts},
  author = {Derks, Peter-Jan H.S. and Townsend-Teague, Alex and Eisert, Jens and Kesselring, Markus S. and Higgott, Oscar and Brown, Benjamin J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2176},
  month = jul,
  year = {2026}
}

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Cited by

[1] Hideyuki Ozawa, Isamu Kudo, Yuki Takeuchi, and Tsuyoshi Yoshida, "Hyperbolic Floquet code with graph-edge syndromes", arXiv:2509.24110, (2025).

[2] Cory T. Aitchison and Benjamin Béri, "Spacetime Spins: Statistical mechanics for error correction with stabilizer circuits", arXiv:2512.21991, (2025).

[3] Jun Zen, Xanda C. Kolesnikow, Campbell K. McLauchlan, Georgia M. Nixon, Thomas R. Scruby, Seok-Hyung Lee, Stephen D. Bartlett, Benjamin J. Brown, and Robin Harper, "Low-valency scalable quantum error correction with a dynamic compass code", arXiv:2604.14299, (2026).

[4] Aleks Kissinger and John van de Wetering, "ZX-Flow: A Flexible Criterion for Deterministic Computation with ZX-Diagrams", arXiv:2603.09580, (2026).

The above citations are from SAO/NASA ADS (last updated successfully 2026-08-12 21:15:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2026-08-12 21:15:34).

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