Partition-based discrete-time quantum walks

  • Norio Konno
  • Renato Portugal
  • Iwao Sato
  • Etsuo Segawa
Article

Abstract

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy’s model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

Keywords

Quantum walk Coined walk Szegedy’s walk Staggered walk Graph tessellation Hypergraph walk Unitary equivalence Intersection graph Bipartite graph 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of EngineeringYokohama National UniversityYokohamaJapan
  2. 2.National Laboratory of Scientific Computing - LNCCPetrópolisBrazil
  3. 3.Oyama National College of TechnologyOyamaJapan
  4. 4.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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