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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.19442 |
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| _version_ | 1866914464368951296 |
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| author | Zhang, Guo Zhu, Yuanye Li, Ying |
| author_facet | Zhang, Guo Zhu, Yuanye Li, Ying |
| contents | 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 $d = Ω(n^{1/a})$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes Zhang, Guo Zhu, Yuanye Li, Ying Quantum Physics 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 $d = Ω(n^{1/a})$. 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. |
| title | Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.19442 |