Random sampling of permutations through quantum circuits
<|reference_start|>Random sampling of permutations through quantum circuits: In this paper, we introduce classical algorithms for random sampling of permutations, drawing inspiration from the Steinhaus-Johnson-Trotter algorithm. Our approach takes a comprehensive view of permutation sampling by expressing them as products of adjacent transpositions. Building on this, we develop a quantum analogue of these classical algorithms using a quantum circuit model for random sampling of permutations for $n$-qubit systems. As an application, we present a quantum algorithm for the two-sample randomization test to assess the difference of means in classical data, utilizing a quantum circuit model. Finally, we propose a nested corona product graph generative model for symmetric groups, which facilitates random sampling of permutations from specific sets of permutations through a quantum circuit model.<|reference_end|>
@article{adhikari2024random,
    title={Random sampling of permutations through quantum circuits},
    author={Bibhas Adhikari},
    journal={arXiv preprint arXiv:2409.03018},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03018},
    primaryClass={quant-ph cs.DM math.CO}
}