Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk

2018/01/18 by Norio Konno, Konno, Norio, Iwao Sato +3
Computer Science · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1801.06209

openalex publication_date 2018/01/18 · openalex created_date 2018/02/02 · openalex updated_date 2026/07/28

Abstract

We obtain a structure theorem of the positive support of the n-th power of the Grover walk on k-regular graph whose girth is greater than 2(n-1). This structure theorem is provided by the parity of the amplitude of another quantum walk on the line which depends only on k. The phase pattern of this quantum walk has a curious regularity. We also exactly show how the spectrum of the n-th power of the Grover walk is obtained by lifting up that of the adjacency matrix to the complex plain.

Citations

• Periodic-Orbit Theory of Anderson Localization on Graphs

Related

• Trapping and spreading properties of quantum walk in homological structure
• A zeta function related to the transition matrix of the discrete-time quantum walk on a graph
• Quantum Walks on Generalized Quadrangles
• Odd-periodic Grover walk
• Periodicity and absolute zeta functions of multi-state Grover walks on cycles