We give an explicit construction to perform any n-qubit computational basis state transposition using Θ(n) gates. This nearly coincides with the lower bound Ω(n/log(nd)) on worst-case and average-case gate complexity to perform transpositions using a d-element gate-set, which we also prove.
@article{arxiv.2309.12820,
title = {Almost-Optimal Computational Basis State Transpositions},
author = {Steven Herbert and Julien Sorci and Yao Tang},
journal= {arXiv preprint arXiv:2309.12820},
year = {2024}
}
Comments
Newest version corrects some minor errors in previous version