Minimum-overlap logical operators for qLDPC codes

Quantum low-density parity-check (qLDPC) codes are a promising candidate for achieving fault-tolerant quantum computation, as they can offer finite encoding rates and good distance scalings. However, qLDPC codes often feature logical operators with high overlap, which leads to correlated logical errors and increases the difficulty of parallelizing quantum gates. In this work, we theoretically investigate techniques to minimize the overlap of logical operators in qLDPC codes. Our methods have the potential to enable more efficient decoding, improved error suppression, and parallelizable gate implementations with qLDPC codes.