### Abstract

We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry is too small to significantly affect the evolution: the system still approximately evolves in its ground and first excited states, rotating to the marked vertex in time π√N/2. Increasing the phase does not change the runtime, but rather changes the support for the 2D subspace, so the system evolves in its first and second excited states, or its second and third excited states, and so forth. Apart from the critical phases corresponding to these transitions in the support, which become more frequent as the phase grows, this reveals that our model of quantum search is robust against time-reversal symmetry breaking.

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

Article number | 405303 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 40 |

DOIs | |

State | Published - Sep 14 2015 |

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 with time-reversal symmetry breaking.** / Wong, Thomas.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Quantum walk search with time-reversal symmetry breaking

AU - Wong, Thomas

PY - 2015/9/14

Y1 - 2015/9/14

N2 - We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry is too small to significantly affect the evolution: the system still approximately evolves in its ground and first excited states, rotating to the marked vertex in time π√N/2. Increasing the phase does not change the runtime, but rather changes the support for the 2D subspace, so the system evolves in its first and second excited states, or its second and third excited states, and so forth. Apart from the critical phases corresponding to these transitions in the support, which become more frequent as the phase grows, this reveals that our model of quantum search is robust against time-reversal symmetry breaking.

AB - We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry is too small to significantly affect the evolution: the system still approximately evolves in its ground and first excited states, rotating to the marked vertex in time π√N/2. Increasing the phase does not change the runtime, but rather changes the support for the 2D subspace, so the system evolves in its first and second excited states, or its second and third excited states, and so forth. Apart from the critical phases corresponding to these transitions in the support, which become more frequent as the phase grows, this reveals that our model of quantum search is robust against time-reversal symmetry breaking.

UR - http://www.scopus.com/inward/record.url?scp=84941773722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941773722&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/40/405303

DO - 10.1088/1751-8113/48/40/405303

M3 - Article

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 40

M1 - 405303

ER -