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Snakes and Ladders: Adapting the Surface Code to Defects

Catherine Leroux1,*, Sophia F. Lin1, Przemyslaw Bienias1, Krishanu R. Sankar1, Asmae Benhemou1,2, Aleksander Kubica1,3, and Joseph K. Iverson1

  • *Contact author: catilero@amazon.com
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PRX Quantum 6, 040302 – Published 2 October, 2025

DOI: https://doi.org/10.1103/815q-xjrb

Abstract

One of the critical challenges solid-state quantum processors face is the presence of fabrication imperfections and two-level systems, which render certain qubits and gates either inoperable or much noisier than tolerable by quantum error-correction protocols. To address this challenge, we develop a suite of novel and highly performant methods for adapting surface code patches in the presence of defective qubits and gates, which we call Snakes and Ladders. We explain how our algorithm generates and compares several strategies in order to find the optimal one for any given configuration of defective components, as well as introduce heuristics to improve runtime and minimize computing resources required by our algorithm. In addition to memory storage we also show how to apply our methods to lattice surgery protocols. Compared to prior works, our methods significantly improve the code distance of the adapted surface code patches for realistic defect rates, resulting in a logical performance similar to that of the defect-free patches.

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Popular Summary

The advantage of quantum computing relies on quantum state superposition and entanglement, which are both fragile to decoherence. Quantum error correction aims at encoding the information redundantly so that errors resulting from either decoherence or controls can be corrected and is therefore essential to build a reliable quantum computer. A promising error-correcting code is the surface code, which uses a two-dimensional array of qubits, the basic unit of quantum information, interacting together via gates. The ability of the surface code to correct errors grows with the size of the surface code patch. A critical challenge for realizing the surface code is the unavoidable presence of nonoperational qubits and gates, which results in holes in the patch that can significantly lower its ability to correct errors.

The ability of the surface code to correct errors relies on measuring multiqubit correlations in groups of two or four via ancillary qubits. In the presence of holes, these correlations grow in size around the holes, making it harder to resolve errors. Larger holes therefore result in lower performance. In this work, we introduce strategies that significantly reduce the size of the holes around nonoperational components, improving the performance of the quantum error-correcting code. Our strategies rely on repurposing ancillary qubits that participate in two correlators instead of a single one. We numerically show that our strategies result in codes that preserve the information with higher fidelity and make the realization of logical operations needed for quantum computing more accessible on near-term devices.

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Outline

Information

PRX Quantum 6, 040302– Published 2 October, 2025
  • Received 21 February 2025
  • Revised 7 August 2025
  • Accepted 28 August 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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