Dumer, Ilya | Engineering Papers

DOE OSTI2011

Design of additive quantum codes via the code-word-stabilized framework

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or nonadditive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Structured error recovery for code-word-stabilized quantum codes

Code-word-stabilized (CWS) codes are, in general, nonadditive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical nonlinear 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 article, we suggest an error grouping technique that allows one 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{sup 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗