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

Yanying Liang; Haoran Zhu

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arXiv · 2607.28521

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

Yanying Liang·Haoran Zhu

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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.

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Yanying Liang, Haoran Zhu. 2026-07-30. Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap. https://arxiv.org/abs/2607.28521

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