Abstract
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are marked by adding elements to them that impart a specific phase shift to the particle as it enters or leaves the edge. If the complete graph has vertices and the subgraph has vertices, the particle becomes localized on the subgraph in steps. This leads to a quantum search that is quadratically faster than a corresponding classical search. We show how to implement the quantum walk using a quantum circuit and a quantum oracle, which allows us to specify the resources needed for a quantitative comparison of the efficiency of classical and quantum searches—the number of oracle calls.
- Received 5 November 2009
DOI:https://doi.org/10.1103/PhysRevA.81.062324
©2010 American Physical Society