### Abstract

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve algorithms. Furthermore, we determine conditions for which spatial search problems on regular graphs are amenable to this doubling of the success probability, and this involves diagrammatically analyzing search using degenerate perturbation theory and deriving a useful formula for how the quantum walk acts in its reduced subspace.

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

Article number | 455301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 45 |

DOIs | |

State | Published - Oct 19 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

*Journal of Physics A: Mathematical and Theoretical*,

*49*(45), [455301]. https://doi.org/10.1088/1751-8113/49/45/455301

**Doubling the success of quantum walk search using internal-state measurements.** / Prusis, Krišjanis; Vihrovs, Jevgenijs; Wong, Thomas.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 49, no. 45, 455301. https://doi.org/10.1088/1751-8113/49/45/455301

}

TY - JOUR

T1 - Doubling the success of quantum walk search using internal-state measurements

AU - Prusis, Krišjanis

AU - Vihrovs, Jevgenijs

AU - Wong, Thomas

PY - 2016/10/19

Y1 - 2016/10/19

N2 - In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve algorithms. Furthermore, we determine conditions for which spatial search problems on regular graphs are amenable to this doubling of the success probability, and this involves diagrammatically analyzing search using degenerate perturbation theory and deriving a useful formula for how the quantum walk acts in its reduced subspace.

AB - In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve algorithms. Furthermore, we determine conditions for which spatial search problems on regular graphs are amenable to this doubling of the success probability, and this involves diagrammatically analyzing search using degenerate perturbation theory and deriving a useful formula for how the quantum walk acts in its reduced subspace.

UR - http://www.scopus.com/inward/record.url?scp=84992731171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992731171&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/45/455301

DO - 10.1088/1751-8113/49/45/455301

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 45

M1 - 455301

ER -