An index theorem for split-step quantum walks

Yasumichi Matsuzawa

An index theorem for split-step quantum walks

Mathematical Physics 2019-07-02 v2 Mesoscale and Nanoscale Physics math.MP Quantum Physics

Authors: Yasumichi Matsuzawa

Abstract

Split-step quantum walks are models of supersymmetric quantum walk, and thus their Witten indices can be defined. We prove that the Witten index of a split-step quantum walk coincides with the difference between the winding numbers of functions corresponding to the right-limit of coins and the left-limit of coins. As a corollary, we give an alternative derivation of the index formula for split-step quantum walks, which is recently obtained by Suzuki and Tanaka.

Keywords

quantum walks

Cite

@article{arxiv.1903.05061,
  title  = {An index theorem for split-step quantum walks},
  author = {Yasumichi Matsuzawa},
  journal= {arXiv preprint arXiv:1903.05061},
  year   = {2019}
}