2020/01/01 by Ada Chan, Chan, Ada, Shaun Fallat +9
Computer Science · #05C50 #15A18 #81P45 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2001.00251
openalex publication_date 2020/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices. We give some basic properties and methods of constructing such graphs. We show that a large class of complex Hadamard diagonalisable graphs have vertex sets forming an equitable partition, and that the Laplacian eigenvalues must be even integers. We provide a number of examples and constructions of complex Hadamard diagonalisable graphs, including two special classes of graphs: the Cayley graphs over ℤrd, and the non--complete extended p--sum (NEPS). We discuss necessary and sufficient conditions for (α, β)--Laplacian fractional revival and perfect state transfer on continuous--time quantum walks described by complex Hadamard diagonalisable graphs and provide examples of such quantum state transfer.