Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound
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Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound
Kenta Kasai
AbstractWe 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.