Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound
This work addresses the challenge of designing efficient quantum error-correcting codes, which is crucial for reliable quantum computing, and represents a significant advancement in this domain-specific area.
The paper tackles the problem of constructing finite-degree quantum LDPC codes with high performance, achieving the Gilbert-Varshamov bound for several finite-degree settings through a rigorous computer-assisted proof.
We construct nested Calderbank-Shor-Steane code pairs with non-vanishing coding rate from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove relative linear distance with high probability. Moreover, for several finite degree settings, we prove Gilbert-Varshamov distance by a rigorous computer-assisted proof.