Efficient ML Decoding for Quantum Convolutional Codes

TL;DR

This paper introduces a new, efficient decoding algorithm for quantum convolutional codes that significantly reduces complexity and enables practical performance evaluation, advancing quantum error correction methods.

Contribution

The paper presents a novel decoding algorithm for quantum convolutional codes that simplifies syndrome mapping and reduces the number of Viterbi algorithm runs needed.

Findings

First performance curve of a general quantum convolutional code

Decoding complexity drastically reduced compared to existing methods

Efficient simulation enabled for quantum convolutional codes

Abstract

A novel decoding algorithm is developed for general quantum convolutional codes. Exploiting useful ideas from classical coding theory, the new decoder introduces two innovations that drastically reduce the decoding complexity compared to the existing quantum Viterbi decoder. First, the new decoder uses an efficient linear-circuits-based mechanism to map a syndrome to a candidate vector, whereas the existing algorithm relies on a non-trivial lookup table. Second, the new algorithm is cleverly engineered such that only one run of the Viterbi algorithm suffices to locate the most-likely error pattern, whereas the existing algorithm must run the Viterbi algorithm many times. The efficiency of the proposed algorithm allows us to simulate and present the first performance curve of a general quantum convolutional code.