Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes

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 dleq wleq 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.