2017/01/28 by Norio Konno, Konno, Norio, Iwao Sato +3
Computer Science · #05C50 #05C60 #15A15 #60F05 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1701.08274
openalex publication_date 2017/01/28 · openalex created_date 2017/02/10 · openalex updated_date 2026/07/28
Recently, the staggered quantum walk (SQW) on a graph is discussed as a generalization of coined quantum walks on graphs and Szegedy walks. We present a formula for the time evolution matrix of a 2-tessellable SQW on a graph, and so directly give its spectra. Furthermore, we present a formula for the Szegedy matrix of a bipartite graph by the same method, and so give its spectra. As an application, we present a formula for the characteristic polynomial of the modified Szegedy matrix in the quantum search problem on a graph, and give its spectra.