Localization does not occur for the Fourier walk on the multi-dimensional lattice
Akihiro Narimatsu
TL;DR
This paper investigates localization phenomena in multi-dimensional lattice quantum walks, establishing conditions for localization and proving that the Fourier walk does not exhibit localization.
Contribution
It provides new conditions for localization in space-homogeneous quantum walks and demonstrates the absence of localization for the Fourier walk in multiple dimensions.
Findings
Localization exists for the Grover walk on multi-dimensional lattices.
Localization does not occur for the Fourier walk on multi-dimensional lattices.
Conditions for localization in space-homogeneous quantum walks are identified.
Abstract
The existence of localization for the Grover walk on the multi-dimensional lattice is known. This paper gives some conditions for the existence of localization for the space-homogeneous quantum walks. We also prove that localization does not occur for the Fourier walk on the multi-dimensional lattice.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum many-body systems