Almost-Optimal Computational Basis State Transpositions

We give an explicit construction to perform any $n$-qubit computational basis state transposition using $\Theta(n)$ gates. This nearly coincides with the lower bound $\Omega(n/\log(nd))$ on worst-case and average-case gate complexity to perform transpositions using a $d$-element gate-set, which we a...

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Bibliographic Details
Main Authors Herbert, Steven, Sorci, Julien, Tang, Yao
Format Journal Article
LanguageEnglish
Published 22.09.2023
Subjects
Physics - Quantum Physics
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Summary:We give an explicit construction to perform any $n$-qubit computational basis state transposition using $\Theta(n)$ gates. This nearly coincides with the lower bound $\Omega(n/\log(nd))$ on worst-case and average-case gate complexity to perform transpositions using a $d$-element gate-set, which we also prove.
DOI:10.48550/arxiv.2309.12820