Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound

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.

Source: arXiv:2603.24588v1 - http://arxiv.org/abs/2603.24588v1 PDF: https://arxiv.org/pdf/2603.24588v1 Original Link: http://arxiv.org/abs/2603.24588v1