Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes

TL;DR

This paper introduces three new fast algorithms for computing the symplectic distance of classical codes associated with quantum stabilizer codes, significantly improving computational efficiency.

Contribution

The paper presents novel algorithms based on Brouwer-Zimmermann for faster distance computation, outperforming existing implementations across various hardware architectures.

Findings

Algorithms are significantly faster than current methods.

Performance gain can exceed an order of magnitude.

Good scalability observed on shared-memory architectures.

Abstract

The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic distance of the associated classical code. Our new algorithms are based on the Brouwer-Zimmermann algorithm. Our experimental study shows that these new implementations are much faster than current state-of-the-art licensed implementations on single-core processors, multicore processors, and shared-memory multiprocessors. In the most computationally-demanding cases, the performance gain in the computational time can be larger than one order of magnitude. The experimental study also shows a good scalability on shared-memory parallel architectures.