Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes

• URL: http://arxiv.org/abs/2510.19442v1
• Date: Wed, 22 Oct 2025 10:15:40 GMT
• Title: Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes
• Authors: Guo Zhang, Yuanye Zhu, Ying Li,
• Abstract summary: 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 $d = Omega(n1/a)$.<n>Results establish a new paradigm for accelerating fault-tolerant quantum computation on qLDPC codes, while maintaining low overhead and broad applicability.
• Score: 4.569242390849337
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $O(d^{a+o(1)})$ for any $[[n,k,d]]$ qLDPC code with constant encoding rate and distance $d = \Omega(n^{1/a})$. For good qLDPC codes, the time overhead is minimized and reaches $O(d^{1+o(1)})$. In contrast, code surgery based on gauging measurement and brute-force branching requires a time overhead of $O(dw^{1+o(1)})$, where $d\leq w\leq n$. 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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