npj Quantum Information, Published online: 20 November 2024; doi:10.1038/s41534-024-00908-8
In this paper, scientists proved a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al.
Their 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 them 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, they were 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., they obtained quantum locally testable codes of new parameters.