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Sparse quantum codes are analogous to LDPC codes in that their check operators require examining only a constant number of qubits. In contrast to LDPC codes, good sparse quantum codes are not known, and even to encode a single qubit, the best known distance is O( n log(n)), due to Freedman, Meyer and Luo. We construct a new family of sparse quantum subsystem codes with minimum distance n 1− for = O(1/ √ log n). A variant of these codes exists in D spatial dimensions and has d = n 1− −1/D ,doi:10.1109/tit.2017.2663199 fatcat:on62ange5zepxptm52upoci3su