Local testability of distance-balanced quantum codes

Abstract

In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. Our technical contribution is that the soundness of the quantum code after this procedure is at least its soundness before the procedure divided by the length of the classical code used to perform distance balancing. This allows us to use any classical code when distance balancing, where previously only the repetition code had been considered for these codes. By using a good classical low-density parity check (LDPC) code, we are able to grow the dimension of the hypersphere product codes and the hemicubic codes while maintaining their distance and locality, but at the expense of soundness. From this, and also by distance balancing a chain complex of Cross et al., we obtain quantum locally testable codes of new parameters.