Handling fabrication defects in hex-grid surface codes

Abstract: Recent work has shown that a hexagonal grid qubit layout, with only three couplers per qubit, is sufficient to implement the surface code with performance comparable to that of a traditional four-coupler layout [McEwen et al., 2023]. In this work we propose a method for handling broken qubits and couplers even in hex-grid surface code architectures, using an extension of the LUCI framework [Debroy et al., 2024]. We show that for isolated broken qubits, the circuit distance drops by one, while for isolated broken couplers, the distance drops by one in one or both bases. By providing a viable dropout strategy, we have removed a critical roadblock to the implementation of hexagonal qubit grids in hardware for large-scale quantum error correction.