Fault-tolerant quantum error correction using error weight parities

TL;DR

This paper introduces weight parity error correction (WPEC), a method for correcting high-weight errors in quantum codes by leveraging error weight parity, applicable to certain concatenated codes and fault-tolerant protocols.

Contribution

The authors propose WPEC, a novel technique that corrects errors of any weight using weight parity information, enhancing fault tolerance in quantum error correction.

Findings

WPEC can correct errors of any weight if error weight parity is known.

Applicable to concatenated codes based on Steane and Golay codes.

Fault-tolerant protocol for [[49,1,9]] code corrects up to 3 faults with minimal ancillas.

Abstract

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different weights are logically equivalent and the same correction procedure is applicable to all equivalent errors, thus correcting high-weight errors is sometimes possible. In this work, we introduce a technique called weight parity error correction (WPEC) which can correct Pauli error of any weight in some stabilizer codes provided that the parity of the weight of the error is known. We show that the technique is applicable to concatenated codes constructed from the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a fault-tolerant error correction protocol using WPEC for the [[49,1,9]] concatenated Steane code which can correct up to 3 faults and requires only 2 ancillas.