The Diamond Protocol: A Planar, Local, and Defect-Adaptive Implementation of Quantum LDPC Codes

Quantum low-density parity-check (qLDPC) codes are a key component for scalable fault-tolerant quantum computation. However, their practical implementation is hindered by geometrically long-range connectivity requirements and a lack of adaptability to hardware defects. In this work, we propose the Diamond Protocol, a systematic method for implementing qLDPC codes on planar hardware restricted to nearest-neighbor connectivity. Our protocol uses graph-theoretic algorithms to compile the stabilizer measurement circuit, partitioning the complete set of stabilizers into a constant number of groups. Each group of stabilizers is then measured simultaneously using a novel Contraction Circuit, a sequence of CNOT and SWAP gates that can be regarded as a generalization of the Hex-grid Circuit used for the surface code. This method provides high flexibility, allowing the circuit to be recompiled to tolerate fabrication defects. We demonstrate the protocol's versatility by constructing efficient, defect-adaptive circuits for Tile Codes with a wide variety of tile weights. Our results provide a concrete path toward the feasible implementation of high-performance qLDPC codes on near-term planar quantum hardware.