## This content will become publicly available on July 8, 2020

# 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:

- The Univ. of Memphis, Memphis, TN (United States)
- 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}

}

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