Quantum Expander Codes

TL;DR

This paper introduces a linear-time decoding algorithm for quantum hypergraph-product LDPC codes that effectively corrects large adversarial errors, leveraging classical code properties.

Contribution

It presents the first efficient linear-time decoding algorithm for quantum hypergraph-product LDPC codes with provable error correction capabilities.

Findings

Decodes adversarial errors of weight Ω(√n)

Runs in linear time relative to the number of qubits

Utilizes expansion properties of classical code factor graphs

Abstract

We present an efficient decoding algorithm for constant rate quantum hypergraph-product LDPC codes which provably corrects adversarial errors of weight $\Omega(\sqrt{n})$ for codes of length $n$. The algorithm runs in time linear in the number of qubits, which makes its performance the strongest to date for linear-time decoding of quantum codes. The algorithm relies on expanding properties, not of the quantum code's factor graph directly, but of the factor graph of the original classical code it is constructed from.