Clustered bounded-distance decoding of codeword-stabilized quantum codes

Codeword stabilized (CWS) codes form a general class of quantum codes that includes stabilizer codes and many families of nonadditive codes with good parameters. Similar to classical nonlinear codes, a CWS code can be decoded by screening all possible errors. For an n-qubit quantum code correcting up to t errors, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. To simplify decoding, we propose an algorithm that employs a single measurement to process all errors located on a given cluster of t qubits. Compared to an exhaustive error screening, this reduces the total number of measurements required for error correction about 3^t times.