Localization of a multi-dimensional quantum walk with one defect

2017/03/13 by Toru Fuda, Fuda, Toru, Daiju Funakawa +3 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1703.04558

openalex publication_date 2017/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schrödinger operator with variable coefficients, which is analyzed using the Feshbach map.

Citations

• The spreading behavior of quantum walks induced by drifted random walks on some magnifier graph

Cited by

• Weak limit theorem for a one-dimensional split-step quantum walk

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• The defect-induced localization in many positions of the quantum random walk