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.

在本文中，我们证明了在 Evra 等人的距离平衡结构下量子局部可测试代码的健全性下限。我们的技术贡献是，此过程后量子代码的健全性至少是它在该程序之前的稳健性除以用于执行距离平衡的经典代码的长度。这允许我们在距离平衡时使用任何经典代码，而以前这些代码只考虑重复代码。通过使用良好的经典低密度奇偶校验 （LDPC） 代码，我们能够增加超球体乘积代码和半三次代码的维度，同时保持它们的距离和位置，但以牺牲可靠性为代价。由此，以及通过 Cross 等人的链复合物的距离平衡，我们获得了新参数的量子局部可测试代码。