Quick Navigation

Topics

Open Quantum Systems Decoherence Quantum Simulation

Limit theorems for quantum walks with memory

arXiv
Authors: Norio Konno, Takuya Machida

Year

2010

Paper ID

9068

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

N/A

Abstract

Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk (QW) with a memory in one dimension. He gave an expression for the amplitude of the QW by path counting method. Moreover he showed that the return probability of the walk is more than 1/2 for any even time. In this paper, we compute the stationary distribution by considering the walk as a 4-state QW without memory. Our result is consistent with his claim. In addition, we obtain the weak limit theorem of the rescaled QW. This behavior is striking different from the corresponding classical random walk and the usual 2-state QW without memory as his numerical simulations suggested.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2010 reference point for readers tracking recent quantum research.
  • Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk (QW) with a memory in one dimension.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

Local Citation Graph (Related-Paper Links)

Current Paper #9068 #68456 Analytic Properties of the Jost... #68455 Mediative Fuzzy Logic: From Typ... #68453 Weak wave turbulence as a precu... #68437 Transition-state lattice modes ...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.