Scattering model for quantum random walks on a hypercube
| Authors | |
|---|---|
| Year of publication | 2005 |
| Type | Article in Periodical |
| Magazine / Source | Physical Review A |
| MU Faculty or unit | |
| Citation | |
| Field | Theoretical physics |
| Keywords | quantum random walk; scattering model |
| Description | Following a recent work by Hillery et al. [Phys. Rev. A 68, 032314 (2003)], we introduce a scattering model of a quantum random walk (SQRW) on a hybercube. We show that this type of quantum random walk can be reduced to the quantum random walk on the line and we derive the corresponding hitting amplitudes. We investigate the scattering properties of the hypercube, connected to the semi-infinite tails. We prove that the SQRW is a generalized version of the coined quantum random walk. We show how to implement the SQRW efficiently using a quantum circuit with standard gates. We discuss one possible version of a quantum search algorithm using the SQRW. Finally, we analyze symmetries that underlie the SQRW and may simplify its solution considerably. |
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