Adaptive surface code for quantum error correction in the presence of temporary or permanent defects

Adam Siegel1,2, Armands Strikis1, Thomas Flatters1, and Simon Benjamin1,2

1Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
2Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom

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Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may correspond to individual qubits or to clusters and could potentially disrupt the code sufficiently to generate logical errors. In this paper, we explore a novel $adaptive$ approach for surface code quantum error correction on a defective lattice. We show that combining an appropriate defect detection algorithm and a quarantine of the identified zone allows one to preserve the advantage of quantum error correction at finite code sizes, at the cost of a qubit overhead that scales with the size of the defect. Our numerics indicate that the code's threshold need not be significantly affected; for example, for a certain scenario where small defects repeatedly arise in each logical qubit, the noise threshold is $2.7\%$ (versus the defect-free case of $2.9\%$). These results pave the way to the experimental implementation of large-scale quantum computers where defects will be inevitable.

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[2] Sengthai Heng, Dongmin Kim, and Youngsun Han, "Mitigating fabrication errors by recovering defective syndrome qubits in surface code", Physical Review A 109 1, 012420 (2024).

[3] Sophia Fuhui Lin, Joshua Viszlai, Kaitlin N. Smith, Gokul Subramanian Ravi, Charles Yuan, Frederic T. Chong, and Benjamin J. Brown, "Codesign of quantum error-correcting codes and modular chiplets in the presence of defects", arXiv:2305.00138, (2023).

[4] Armands Strikis, Simon C. Benjamin, and Benjamin J. Brown, "Quantum Computing is Scalable on a Planar Array of Qubits with Fabrication Defects", Physical Review Applied 19 6, 064081 (2023).

[5] M. B. Hastings, "Quantum Codes on Graphs", arXiv:2308.10264, (2023).

[6] David Aasen, Jeongwan Haah, Parsa Bonderson, Zhenghan Wang, and Matthew Hastings, "Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits", arXiv:2307.03715, (2023).

[7] Asmae Benhemou, Kaavya Sahay, Lingling Lao, and Benjamin J. Brown, "Minimising surface-code failures using a color-code decoder", arXiv:2306.16476, (2023).

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