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

2024-08-20

arXiv.org

AI Summary

To address the low computational efficiency of minimum distance calculation for stabilizer quantum codes, this paper proposes three novel algorithms built upon the Brouwer–Zimmermann framework: an enhanced single-threaded algorithm, a preprocessing strategy leveraging symmetry-group reduction, and a shared-memory parallel search with memory optimization. The core method reformulates the quantum code minimum distance problem as classical symplectic distance computation, significantly reducing the search space via structural symmetry-based pruning and load-balanced parallelization. Experimental results demonstrate over 10× speedup over state-of-the-art methods on high-dimensional, complex codes, and near-linear scalability across multicore platforms. This work delivers the first efficient, scalable, and exact minimum distance computation tool for stabilizer quantum codes, enabling practical design and rigorous evaluation of quantum error-correcting codes.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Develop fast algorithms for quantum code distance computation
• Improve symplectic distance calculation for classical codes
• Enhance performance on single-core and parallel processors

Innovation

• Fast symplectic distance computation algorithms
• Based on Brouwer-Zimmermann algorithm
• High scalability on parallel architectures