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Title: Continuous-time quantum walks on dynamic graphs

Abstract

Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Lastly, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.

Authors:
 [1]; ORCiD logo [2]
  1. The Univ. of Memphis, Memphis, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS) (SC-27)
OSTI Identifier:
1542242
Alternate Identifier(s):
OSTI ID: 1546367
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 100; Journal Issue: 1; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 96 KNOWLEDGE MANAGEMENT AND PRESERVATION

Citation Formats

Herrman, Rebekah, and Humble, Travis S. Continuous-time quantum walks on dynamic graphs. United States: N. p., 2019. Web. doi:10.1103/PhysRevA.100.012306.
Herrman, Rebekah, & Humble, Travis S. Continuous-time quantum walks on dynamic graphs. United States. doi:10.1103/PhysRevA.100.012306.
Herrman, Rebekah, and Humble, Travis S. Mon . "Continuous-time quantum walks on dynamic graphs". United States. doi:10.1103/PhysRevA.100.012306.
@article{osti_1542242,
title = {Continuous-time quantum walks on dynamic graphs},
author = {Herrman, Rebekah and Humble, Travis S.},
abstractNote = {Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Lastly, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.},
doi = {10.1103/PhysRevA.100.012306},
journal = {Physical Review A},
number = 1,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
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