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Structured Error Recovery for Codeword-Stabilized Quantum Codes

  • Li, Yunfan
  • Dumer, Ilya
  • Grassl, Markus
  • Pryadko, Leonid P.
Published Article
Publication Date
Mar 08, 2010
Submission Date
Dec 16, 2009
DOI: 10.1103/PhysRevA.81.052337
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Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.

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