1 citations · 1 across the 14 of their papers we have counts for
15 papers
The diffusive spectral gap of the qubit eSWAP chain
Yanying Liang, Haoran Zhu
We prove that the second-moment Hamiltonian of the open qubit eSWAP chain has a diffusive spectral gap, resolving a conjecture of Li, Zheng, Liu, Jiang, and Liu. We also characteri…
The maximum relaxation time of a random walk on regular graphs
Haoran Zhu
We establish sharp quadratic bounds on the relaxation time of simple random walk on connected regular graphs, with leading constants and for even and odd orders,…
Universal Plücker positivity and the Octopus inequality
Haoran Zhu
We prove a positivity theorem for the universal Plücker coordinates of Karp and Purbhoo when exactly one parameter is negative, with a sharp uniform threshold governed by the large…
Random walks on wreath products and spectral gaps for coloured interchange processes
Haoran Zhu
We introduce group-valued coloured interchange processes, a class of continuous-time random walks on wreath products generated by transpositions and arbitrary symmetric base-group…
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
We prove that every ironed two-qubit gadget whose KAK-derived parameter satisfies has, on the complete graph with , the same second-moment spectral gap…
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{sl…
Aldous property for full-flag Johnson graphs
Gary Greaves, Haoran Zhu
We show that the full-flag Johnson graph has spectral gap equal to that of its Schreier quotient arising from the point-stabiliser equitable partition. Our results confirm two conj…
BiHom-Lie brackets and the Toda equation
Botong Gai, Chuanzhong Li, Jiacheng Sun +2
We introduce a BiHom-type skew-symmetric bracket on built from two commuting inner automorphisms and with and integer…
Matrices as graded BiHom-algebras and decompositions
Jiacheng Sun, Shuanhong Wang, Haoran Zhu
We present matrices as graded regular BiHom-associative algebras and study several features of their decompositions. More precisely, we introduce a notion of connection in the supp…
Sweedler duality for Hom-(co)algebras and Hom-(co)modules
Jiacheng Sun, Shuanhong Wang, Chi Zhang +1
We establish a dual version of infinite-dimensional Hom-algebras and Hom-modules by using the Sweedler duality construction. Additionally, linear morphisms between infinite-dimensi…
On an optimal problem of bilinear forms
Naihuan Jing, Yibo Liu, Jiacheng Sun +2
We study an optimization problem originated from the Grothendieck constant. A generalized normal equation is proposed and analyzed. We establish a correspondence between solutions…