One-dimensional quantum walks via generating function and the CGMV method

Norio Konno, Etsuo Segawa

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We treat quantum walk (QW) on the line whose quantum coin at each vertex tends to the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law" decay around the origin and a "strongly" ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with linear scaling whose density has two delta measures at x = 0 (the origin) and x = 1 (the bottom) without continuous parts.

Original languageEnglish
Pages (from-to)1165-1186
Number of pages22
JournalQuantum Information and Computation
Issue number13-14
Publication statusPublished - 2014 Oct 1


  • CMV matrix
  • Generating function
  • Quantum walk

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Computational Theory and Mathematics


Dive into the research topics of 'One-dimensional quantum walks via generating function and the CGMV method'. Together they form a unique fingerprint.

Cite this