Faster quantum walk algorithm for the two dimensional spatial search

Details Faster quantum walk algorithm for the two dimensional spatial search Faster quantum walk algorithm for the two dimensional spatial search

2008-01-03

arxiv.org/abs/0801.0497v2

Physics

Quantum Physics

7 pages, 1 figure. Accepted for publication in PRA

Scientific paper

10.1103/PhysRevA.78.012310

We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve this problem, and it is an open question whether the performance can be improved. We present a new algorithm which solves the problem in $O(\sqrt{N\log N})$ steps, thus giving an $O(\sqrt{\log N})$ improvement over the known algorithms. The improvement is achieved by controlling the quantum walk on the lattice using an ancilla qubit.

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