Physics – Quantum Physics
Scientific paper
2009-11-05
Physics
Quantum Physics
4 pages, 2 figures
Scientific paper
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 N vertices and the subgraph has K vertices, the particle becomes localized on the subgraph in O(N/K) 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 resource needed for a quantitative comparison of the efficiency of classical and quantum searches -- the number of oracle calls.
Buzek Vladimir
Hillery Mark
Reitzner Daniel
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