### Abstract

Quantum random walks have received much attention for their intrinsic interest and many possible uses and have been experimentally demonstrated. In this work we look at the possibility of using a biased one-dimensional (1D) quantum walk as an element within a larger quantum device. We ask whether one can use a quantum walk to act as a router with one bias setting engineering the quantum walk to route probability flow one direction while another bias setting routes flow in the opposite direction. Appealing to electrical circuit terminology, we consider a biased quantum walk over a large spatial lattice to act as a single "lumped element" whose routing action depends on the coin bias. We discover that the lumped-element current, when summed over the quantum walk lattice, reaches a steady state and for specific initial states we derive an analytic form for this steady-state lumped-element current. We show that we can control the magnitude and the direction (routing) of the steady-state current. Curiously the control phase and steady-state total current exhibits a sinusoidal current-phase relationship indicating that the lumped element may be similar to that found in Josephson junctions. Finally we illustrate that conservative 1D Hamiltonian systems can also exhibit steady-state dynamics similar to the quantum walk.

Original language | English |
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Article number | 012339 |

Pages (from-to) | 012339-1-012339-8 |

Number of pages | 8 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 90 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Jul 2014 |

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*90*(1), 012339-1-012339-8. [012339]. https://doi.org/10.1103/PhysRevA.90.012339