## Abstract

We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and generalized amplitude damping channel. Explicit expressions for the probability distribution of QWs on a line and on a cyclic path are derived under localized and delocalized initial states. We show that QWs which begin from a delocalized state generate mixture probability distributions, which could give rise to useful algorithmic applications related to data encoding schemes. Specifically, we show how the combination of delocalzed initial states and decoherence can be used for computing the binomial transform of a given set of numbers. However, the sensitivity of QWs to noisy environments may negatively affect various other applications based on QWs.

Original language | English |
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Pages (from-to) | 236-250 |

Number of pages | 15 |

Journal | Optics |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2021 |

### Bibliographical note

Publisher Copyright:© 2021 by the authors.

## Keywords

- decoherence
- quantum walks
- quantum-to-classical transition