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Bibliographic Details
Main Author: Hanson, Jason
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.11938
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Table of Contents:
  • Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm constructs a circuit from any decomposition of the permutation into a product of transpositions, but uses one ancilla line. The second, which uses no ancillae, constructs a circuit from a decomposition into a product of transpositions that have a Hamming distance of one. We show that any permutation admits such a decomposition, and we give a strategy for reducing the number of transpositions involved.