Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes
<|reference_start|>Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes: 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.<|reference_end|>
@article{hernando2024fast,
    title={Fast Algorithms and Implementations for Computing the Minimum Distance
  of Quantum Codes},
    author={Fernando Hernando, Gregorio Quintana-Ort'i, Markus Grassl},
    journal={arXiv preprint arXiv:2408.10743},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.10743},
    primaryClass={quant-ph cs.CE cs.IT cs.MS math.IT}
}