On the support of the Grover walk on higher-dimensional lattices

2020/01/28 by Norio Konno, Konno, Norio, Sarato Takahashi +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2001.10261

openalex publication_date 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents the minimum supports of states for stationary measures of the Grover walk on the d-dimensional lattice by solving the corresponding eigenvalue problem. The numbers of the minimum supports for moving and flip-flop shifts are 2^d (d ge 1) and 4 (d ge 2), respectively.

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