Crossovers induced by discrete-time quantum walks

  • Authors:

  • Kota Chisaki;Norio Konno;Etsuo Segawa;Yutaka Shikano

  • Affiliations:

  • Department of Applied Mathematics, Yokohama National University, Hodogaya, Yokohama, Japan;Department of Applied Mathematics, Yokohama National University, Hodogaya, Yokohama, Japan;Department of Mathematical Informatics, The University of Tokyo, Tokyo, Japan;Department of Physics, Tokyo Institute of Technology, Tokyo, Japan and Department of Mathematical Engineering, Massachusetts Institute of Technology

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2011

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Abstract

We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A 81, 062129 (2010)] on the DTQW with position measurements. We show that the position measurements per each step with probability p ∼ 1/nβ can be evaluated, where n is the final time and 0