### Abstract

The Johnson graph J (n, k) is defined by n symbols, where vertices are kelement subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J (n, 1) is the complete graph Kn, and J (n, 2) is the strongly regular triangular graph Tn, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J (n, 3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J (n, k) with fixed k.

Original language | English (US) |
---|---|

Article number | 195303 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 19 |

DOIs | |

State | Published - Apr 12 2016 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

**Quantum walk search on Johnson graphs.** / Wong, Thomas.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 49, no. 19, 195303. https://doi.org/10.1088/1751-8113/49/19/195303

}

TY - JOUR

T1 - Quantum walk search on Johnson graphs

AU - Wong, Thomas

PY - 2016/4/12

Y1 - 2016/4/12

N2 - The Johnson graph J (n, k) is defined by n symbols, where vertices are kelement subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J (n, 1) is the complete graph Kn, and J (n, 2) is the strongly regular triangular graph Tn, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J (n, 3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J (n, k) with fixed k.

AB - The Johnson graph J (n, k) is defined by n symbols, where vertices are kelement subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J (n, 1) is the complete graph Kn, and J (n, 2) is the strongly regular triangular graph Tn, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J (n, 3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J (n, k) with fixed k.

UR - http://www.scopus.com/inward/record.url?scp=84964553207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964553207&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/19/195303

DO - 10.1088/1751-8113/49/19/195303

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 19

M1 - 195303

ER -