Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap

Abstract:We prove that every ironed two-qubit gadget whose KAK-derived parameter satisfies $a=5/9$ has, on the complete graph $K_n$ with $n\geqslant 5$, the same second-moment spectral gap as the iSWAP gadget. The central step is a representation-theoretic localisation theorem: the largest strictly negative eigenvalue of the associated $\mathfrak S_n$-invariant operator always occurs in the highest-spin $\mathrm{SU}(2)$ summand. A local positive-semidefinite decomposition separates every spin sector except the two highest. This settles a conjecture of Kong, Li, and Liu.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Spectral Theory (math.SP)

arXiv:2607.28521 [quant-ph]

(or arXiv:2607.28521v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.28521 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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