The generator and quantum Markov semigroup for quantum walks

Chul Ki Ko, Hyun Jae Yoo

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The quantum walks in the lattice spaces are represented as unitary evolutions. We find a generator for the evolution and apply it to further understand the walks. We first extend the discrete time quantum walks to continuous time walks. Then we construct the quantum Markov semigroup for quantum walks and characterize it in an invariant subalgebra. In the meanwhile, we obtain the limit distributions of the quantum walks in one-dimension with a proper scaling, which was obtained by Konno by a different method.

Original languageEnglish
Pages (from-to)363-385
Number of pages23
JournalKodai Mathematical Journal
Volume36
Issue number2
DOIs
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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