Clustered Error Correction of Codeword-Stabilized Quantum Codes

TL;DR

This paper introduces an efficient error correction algorithm for codeword stabilized quantum codes that significantly reduces the number of measurements needed for error recovery, enhancing quantum error correction efficiency.

Contribution

It presents a novel algorithm for correcting all t-qubit errors in CWS codes using a single measurement per set, reducing measurement complexity compared to exhaustive methods.

Findings

Reduces measurement count by a factor of about 3^t

Applicable to a broad class of quantum codes including non-additive ones

Improves efficiency of quantum error correction procedures

Abstract

Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of t qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about 3^t.