Quantum computation and quantum information
Quantum computation and quantum information
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Time-varying periodic convolutional codes with low-density parity-check matrix
IEEE Transactions on Information Theory
Nonbinary quantum stabilizer codes
IEEE Transactions on Information Theory
Sparse-graph codes for quantum error correction
IEEE Transactions on Information Theory
LDPC block and convolutional codes based on circulant matrices
IEEE Transactions on Information Theory
On the construction of stabilizer codes with an arbitrary binary matrix
Quantum Information Processing
A class of quantum low-density parity check codes by combining seed graphs
Quantum Information Processing
On nonbinary quantum convolutional BCH codes
Quantum Information & Computation
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Existing quantum stabilizer codes constructed from the classic binary codes exclusively belong to the special subclass of Calderbank-Shor-Steane (CSS) codes. This paper fills in the gap by proposing five systematic constructions for non-CSS stabilizer codes, the first four of which are based on classic binary quasi-cyclic low-density parity-check (LDPC) codes and last on classic binary LDPC-convolutional codes. These new constructions exploit structured sparse graphs, make essential use of simple and powerful coding techniques including concatenation, rotation and scrambling, and generate rich classes of codes with a wide range of lengths and rates. We derive the sufficient, and in some cases also the necessary, conditions for each construction to satisfy the general symplectic inner product (SIP) condition, and develop practical decoder algorithms for these codes. The resulting codes are the first classes of non-CSS quantum LDPC codes and non-CSS quantum convolutional codes rooted from classic binary codes (rather than codes in GF(4)), and some of them perform as well as or better than the existing quantum codes.