Optimal number of stabilizer measurement rounds in an idling surface code patch

Áron Márton; János K. Asbóth

doi:10.22331/q-2025-06-12-1767

Optimal number of stabilizer measurement rounds in an idling surface code patch

Áron Márton¹ and János K. Asbóth^1,2,3

¹Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
²HUN-REN Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49., Hungary
³HUN-REN-BME-BCE Quantum Technology Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary

Published:	2025-06-12, volume 9, page 1767
Editor:	Joschka Roffe
Eprint:	arXiv:2408.07529v4
Doi:	https://doi.org/10.22331/q-2025-06-12-1767
Citation:	Quantum 9, 1767 (2025).

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Abstract

Logical qubits can be protected against environmental noise by encoding them into a highly entangled state of many physical qubits and actively intervening in the dynamics with stabilizer measurements. In this work, we numerically optimize the rate of these interventions: the number of stabilizer measurement rounds for a logical qubit encoded in a surface code patch and idling for a given time. We model the environmental noise on the circuit level, including gate errors, readout errors, amplitude and phase damping. We find, qualitatively, that the optimal number of stabilizer measurement rounds is getting smaller for better qubits and getting larger for better gates or larger code sizes. We discuss the implications of our results to some of the leading architectures, superconducting qubits, and neutral atoms.

Featured image: Numerically obtained logical failure rates, for three different sets of parameters, plotted against the number of measurement rounds. The black intervals around the minima of the curves depict the optimal number of stabilizer measurement rounds, within uncertainty. The three different curves show that for better qubits (larger $T_1$), the optimal number increases, whereas for better gates (lower $p$), it decreases.

Popular summary

Quantum computers are expected to solve certain problems that are too difficult for classical computers. However, to build a reliable quantum device from noisy physical components, quantum error correction is essential. One promising strategy is to encode information in many physical qubits using a quantum error-correcting code, and then repeatedly measure special multi-qubit operators—called stabilizers—to detect errors. In this work, we numerically optimize how often these stabilizer measurements should be performed for a logical qubit that is idling for a fixed amount of time. We focus on the surface code, one of the most popular error-correcting codes, and simulate its performance under realistic circuit-level noise. Our results show that the optimal number of stabilizer measurement rounds decreases as physical qubits become less noisy, but increases with better gate fidelity or when more physical qubits are used. We discuss the practical implications of these findings for leading quantum computing platforms such as superconducting qubits and neutral atom systems.

► BibTeX data

@article{Marton2025optimalnumberof,
  doi = {10.22331/q-2025-06-12-1767},
  url = {https://doi.org/10.22331/q-2025-06-12-1767},
  title = {Optimal number of stabilizer measurement rounds in an idling surface code patch},
  author = {M{\'{a}}rton, {\'{A}}ron and Asb{\'{o}}th, J{\'{a}}nos K.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1767},
  month = jun,
  year = {2025}
}

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[1] Liran Shirizly, Dekel Meirom, Malcolm Carroll, and Haggai Landa, "Feedforward suppression of readout-induced faults in quantum error correction", Physical Review A 112 5, L050602 (2025).

[2] Satvik Maurya and Swamit Tannu, "Synchronization for Fault-Tolerant Quantum Computers", arXiv:2506.10258, (2025).

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