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  • Open Access

Accelerating Fault-Tolerant Quantum Computation with Good Quantum Low-Density Parity-Check Codes

Guo Zhang, Yuanye Zhu, and Ying Li*

  • *Contact author: yli@gscaep.ac.cn
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PRX Quantum 7, 033012 – Published 8 July, 2026

DOI: https://doi.org/10.1103/3fj5-gn1h

Abstract

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of O(da+o(1)) for any [[n,k,d]] qLDPC code with constant encoding rate and distance d=Ω(n1/a). For good qLDPC codes, the time overhead is minimized and reaches O(d1+o(1)). In contrast, code surgery based on gauging measurement and brute-force branching requires a time overhead of O(dw1+o(1)), where d≤w≤n. Thus, our scheme is asymptotically faster for all codes with a<2. This speedup is achieved by developing techniques that enable parallelized code surgery under constant qubit overhead and leverage classical locally testable codes for efficient resource state preparation. These results establish a new paradigm for accelerating fault-tolerant quantum computation on qLDPC codes, while maintaining low overhead and broad applicability.

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Popular Summary

Building a large-scale quantum computer requires it to operate reliably despite physical errors capability known as fault tolerance. Yet fault-tolerant schemes inevitably require extra qubits and additional computation time, making it challenging to keep overall resource overhead low. In this work, we introduce a scheme that enables fault-tolerant quantum computation (FTQC) with constant qubit overhead and minimized time overhead, surpassing existing methods in asymptotic efficiency. This advance is enabled by two new techniques, parallelized code surgery and locally testable state preparation, which apply broadly to quantum low-density parity-check (qLDPC) codes, a highly promising family of codes defined by their sparse structure. We also provide a rigorous proof of fault tolerance, ensuring reliable protection of quantum information throughout computation. Our protocol achieves a time overhead of O(d1+o(1)) for all good qLDPC codes, where d is the code distance. Yet approaching constant time overhead remains an open challenge. We conjecture that combining our techniques with other emerging ideas in quantum error correction could bring this milestone closer, marking an exciting next step toward scalable, low-overhead quantum computing.

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Outline

Information

PRX Quantum 7, 033012– Published 8 July, 2026
  • Received 17 November 2025
  • Revised 5 April 2026
  • Accepted 3 June 2026
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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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