Faster quantum-walk algorithm for the two-dimensional spatial search
Faster quantum-walk algorithm for the two-dimensional spatial search
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N}\ifmmode\times\else\texttimes\fi{}\sqrt{N}$. The previous quantum-walk based algorithms take $O(\sqrt{N}\text{ }\text{ln}\text{ }N)$ steps to solve this problem, and it is an open question whether the performance can be improved. …