Abstract
We consider the problem of finding a desired item out of items arranged on the sites of a two-dimensional lattice of size . The previous quantum-walk based algorithms take steps to solve this problem, and it is an open question whether the performance can be improved. We present an algorithm which solves the problem in steps, thus giving an improvement over the known algorithms. The improvement is achieved by controlling the quantum walk on the lattice using an ancilla qubit.
- Received 3 January 2008
DOI:https://doi.org/10.1103/PhysRevA.78.012310
©2008 American Physical Society