Structured Error Recovery for Codeword-Stabilized Quantum Codes

TL;DR

This paper introduces a structured error recovery method for codeword stabilized quantum codes that significantly reduces the number of measurements needed for error correction, enhancing efficiency especially for additive codes.

Contribution

It proposes an error grouping technique that allows simultaneous testing of large error groups, exponentially decreasing measurement complexity for CWS codes.

Findings

Reduces measurements by approximately 3^t times for error correction.

Equivalent to syndrome-based recovery for additive CWS codes.

Improves efficiency of error correction in non-additive quantum codes.

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.