From the 1 of 10 linked papers with an AI index.
10 papers
iSWAP maximises the second-moment spectral gap in random quantum circuits
Yanying Liang, Haoran Zhu
We prove that the gate maximises the spectral gap of the Hermitian second-moment operator on every connected graph with at least three vertices, among all two-loca…
Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap
Yanying Liang, Haoran Zhu
The paper proves that ironed two‑qubit gadgets with KAK parameter a=5/9 have the same second‑moment spectral gap as the iSWAP gadget on complete graphs with at least five vertices,…
The Hurwitz sum-of-squares problem depends on the base field
Chi Zhang, Haoran Zhu
We show that the Hurwitz problem for sums of squares can depend on the base field. More precisely, we construct an explicit formula of type over every field of charact…
Spectral gap of biased adjacent-transposition chains
Gary R. W. Greaves, Haoran Zhu
We establish a sharp lower bound on the spectral gap of the biased adjacent-transposition Markov chain on the symmetric group. As a consequence, we resolve a longstanding conjectur…
A symmetry formula for correlation functions in the superintegrable chiral Potts spin chain
Haoran Zhu
We prove an exact finite-volume symmetry formula for two-point functions in the periodic -state superintegrable chiral Potts spin chain. We show that, for every chain length …
Infinitesimal deformations of with a twisted Jacobi identity
Haoran Zhu
We show that whenever \[ [\,\cdot,\cdot]_t = [\,\cdot,\cdot]_0 + t[\,\cdot,\cdot]_1,\qquad α_t = \mathrm{id} + tα_1 \] define an infinitesimal Hom--Lie deformation of $\mathfrak{…