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Boundary-induced coherence in the staggered quantum walk on different topologies

Khatibi Moqadam, J ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevA.98.012123
  3. Publisher: American Physical Society , 2018
  4. Abstract:
  5. The staggered quantum walk is a type of discrete-time quantum-walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered dynamics on a two-dimensional lattice composed of superconducting microwave resonators connected with tunable couplings. The naive generalization of the one-dimensional staggered dynamics generates two uncoupled one-dimensional quantum walks; thus more complex partitions need to be employed. However, by analyzing the coherence of the dynamics, we show that the quantumness of the evolution corresponding to two independent one-dimensional quantum walks can be elevated to the level of a single two-dimensional quantum walk, only by modifying the boundary conditions. In fact, by changing the lattice boundary conditions (or topology), we explore the walk on different surfaces such as a torus, a Klein bottle, a real projective plane, and a sphere. The coherence and the entropy reach different levels depending on the topology of the surface. We observe that the entropy captures similar information as coherence; thus we use it to explore the effects of boundaries on the dynamics of the continuous-time quantum walk and the classical random walk. © 2018 American Physical Society
  6. Keywords:
  7. Bottles ; Boundary conditions ; Continuous time systems ; Dynamics ; Entropy ; Microwave devices ; Microwave resonators ; Superconducting resonators ; Topology ; Continuous-time quantum walks ; Discrete time ; Klein bottles ; Quantum walk ; Real projective plane ; Superconducting microwave resonators ; Tunable coupling ; Two-dimensional lattices ; Quantum theory
  8. Source: Physical Review A ; Volume 98, Issue 1 , July , 2018 ; 24699926 (ISSN)
  9. URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.012123