Improved qLDPC surgery for logical measurements and gates

In the last few years, quantum LDPC codes have developed to become serious contenders for the fault-tolerant architecture needed to build a large-scale quantum computer. Perhaps the frontier of qLDPC code research concerns performing logical measurements and gates fault-tolerantly with minimal additional overhead. Here I present the gauge-fixed qLDPC surgery scheme introduced in arXiv:2407.18393 as a solution to this problem. In a specific case, the 144 qubit gross code from Bravyi et al.~(Nature 627, 778-782), we can perform all Clifford gates on 11 logical qubits using just 103 additional qubits and checks. In general, gauge-fixed qLDPC surgery can be used to perform arbitrary logical measurements on arbitrary qLDPC codes, though it relies on structure of the code to ensure the process remains qLDPC. In certain cases where the code's Tanner graph exhibits edge expansion, the scheme is fault-tolerant with distance d using just O(d) additional qubits and checks. Subsequent works (2410.02213 and 2410.03628) have removed all requirements on original code structure while still requiring just quasi-linear additional space overhead. This makes qLDPC surgery a promising approach to fault-tolerant computation with arbitrary qLDPC codes.