Quantum Error Correction via Noise Guessing Decoding

TL;DR

This paper introduces a quantum-GRAND decoding strategy for quantum error correction codes, enabling near-optimal performance at any code length and adapting to changing quantum noise conditions.

Contribution

It extends classical noise guessing decoding to quantum codes, allowing efficient, adaptive decoding of quantum random linear codes with practical noise statistics.

Findings

Quantum-GRAND achieves near-maximum performance for QRLCs.

The proposed method enables adaptive decoding based on quantum noise statistics.

Assessment of circuit complexity for QRLCs to reach asymptotic performance.

Abstract

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to efficiently decode classical random linear codes (RLCs) performing near the maximum rate of the finite blocklength regime. By using noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, provided that a simple code membership test exists. These conditions are particularly suitable for quantum systems, and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum-GRAND, this work shows that it is possible to decode QECCs that are easy to adapt to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum-GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding.