iSWAP maximises the second-moment spectral gap in random quantum circuits

Abstract:We prove that the $\mathrm{iSWAP}$ gate maximises the spectral gap of the Hermitian second-moment operator on every connected graph with at least three vertices, among all two-local unitary circuit ensembles. We further prove that the polyhedral cone defined by asymmetric four-point inequalities is invariant under the transpose of the $\mathrm{iSWAP}$ semigroup, yielding a componentwise comparison certificate for its positive Perron--Frobenius eigenvector. These results resolve a conjecture of Kong, Li, and Liu.

arXiv:2607.29551 [quant-ph]

(or arXiv:2607.29551v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.29551 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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