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  • Open Access

Surface Code with Imperfect Erasure Checks

Kathleen Chang1,2,*, Shraddha Singh3,2, Jahan Claes3,2, Kaavya Sahay3,2, James Teoh4, and Shruti Puri3,2

  • 1Yale University, Department of Physics, New Haven, Connecticut 06520, USA
  • 2Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
  • 3Yale University, Department of Applied Physics, New Haven, Connecticut 06520, USA
  • 4Quantum Circuits, Inc., 25 Science Park, New Haven, Connecticut 06511, USA

  • *Contact author: katie.chang@yale.edu
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PRX Quantum 6, 040355 – Published 4 December, 2025

DOI: https://doi.org/10.1103/d1v7-nctj

Abstract

Recently, significant effort has been devoted towards designing erasure qubits in which dominant physical noise excites detectable leakage states that can be returned to the qubit subspace. Interest in these erasure qubits has been driven by studies showing that the requirements for fault-tolerant quantum error correction are significantly relaxed when noise in every gate operation is dominated by erasures. However, these studies assume perfectly accurate erasure checks after every gate operation which generally come with undesirable time and hardware overhead costs. In this work, we investigate the consequences of using an imperfect but overhead-efficient erasure check for fault-tolerant quantum error correction with the surface code. We show that, under physically reasonable assumptions on the imperfect erasure checks, the threshold error rate is still at least over twice that for Pauli noise. We also study the impact of imperfect erasure checks on the effective error distance and find that it degrades the effective distance under a general error model in which a qubit suffers from depolarizing noise when interacting with a leaked qubit. We then identify a more restrictive but realistic noise model for a qubit that interacts with a leaked qubit, under which the effective error distance is twice that for Pauli noise. We apply our analysis to recently proposed superconducting dual-rail erasure qubits and show that achieving good-performance surface code quantum memories with relaxed system requirements is possible.

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Physics Subject Headings (PhySH)

Popular Summary

Quantum error-correcting codes are required to build scalable quantum computers; however, implementing them incurs significant space and time overhead. A promising route toward reducing this overhead is using erasure qubits, which are engineered such that the dominant noise process takes qubits to detectable leakage states. By intermittently performing erasure checks that identify qubits in these states, one can infer when and where errors occur. This additional information allows erasures to be corrected more efficiently than standard Pauli errors, which are unheralded bit- or phase-flip errors.

Previous analyses of erasure qubits typically assume that erasure checks are performed with perfect accuracy, neglecting the cost of performing frequent, high-fidelity checks in real hardware. In this work, we analyze the impact of imperfect but overhead-efficient erasure checks on the performance of the surface code, a leading quantum error-correcting code. We show that, under realistic physical assumptions, the error threshold remains more than twice as high as for standard Pauli noise, demonstrating that erasure-based architectures retain a substantial advantage even with imperfect checks.

Another important metric is the effective distance, which determines how many errors a code can correct. Idealized erasures double the effective distance compared to Pauli noise. We find that, for physically motivated imperfect checks, this doubling persists. By applying results to recently proposed superconducting dual-rail erasure qubits, we find that one can reap the benefits of an erasure architecture even with relaxed system requirements and realistically imperfect erasure checks, establishing erasure platforms as a viable and efficient path toward scalable, fault-tolerant quantum computation.

See Also

Optimizing Quantum Error-Correction Protocols with Erasure Qubits

Shouzhen Gu, Yotam Vaknin, Alex Retzker, and Aleksander Kubica
PRX Quantum 6, 040354 (2025)

Article Text

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PRX Quantum 6, 040355– Published 4 December, 2025
  • Received 16 September 2024
  • Revised 29 August 2025
  • Accepted 8 October 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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