### Abstract

A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.

Original language | English |
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Pages (from-to) | 100-104 |

Number of pages | 5 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 379 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 23 2015 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*379*(3), 100-104. https://doi.org/10.1016/j.physleta.2014.11.001

**Unitary equivalence of quantum walks.** / Goyal, Sandeep K.; Konrad, Thomas; Diósi, L.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 379, no. 3, pp. 100-104. https://doi.org/10.1016/j.physleta.2014.11.001

}

TY - JOUR

T1 - Unitary equivalence of quantum walks

AU - Goyal, Sandeep K.

AU - Konrad, Thomas

AU - Diósi, L.

PY - 2015/1/23

Y1 - 2015/1/23

N2 - A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.

AB - A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.

UR - http://www.scopus.com/inward/record.url?scp=84912571191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84912571191&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2014.11.001

DO - 10.1016/j.physleta.2014.11.001

M3 - Article

AN - SCOPUS:84912571191

VL - 379

SP - 100

EP - 104

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 3

ER -