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arXiv · 0912.3245

Structured Error Recovery for Codeword-Stabilized Quantum Codes

Yunfan Li·Ilya Dumer·Markus Grassl·Leonid P. Pryadko
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Abstract

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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Yunfan Li, Ilya Dumer, Markus Grassl, Leonid P. Pryadko. 2010-03-08. Structured Error Recovery for Codeword-Stabilized Quantum Codes. https://doi.org/10.1103/physreva.81.052337

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