2024/09/04 by Bibhas Adhikari, Adhikari, Bibhas
Biochemistry, Genetics and Molecular Biology · Computer Science · #Combinatorics (math.CO) #DNA and Biological Computing #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fractal and DNA sequence analysis #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2409.03018
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a classical algorithm 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 the classical algorithm using a quantum circuit model for random sampling of permutations. As an application, we present a quantum algorithm for the two-sample randomization test to assess the difference of means in classical data. 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.