Tulsi, Avatar (2008) Faster quantum-walk algorithm for the two-dimensional spatial search. In: Physical Revoew A, 78 (1). 012310-1- 012310-6.
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We consider the problem of finding a desired item out of N items arranged on the sites of a two-dimensional lattice of size root N X root N. The previous quantum-walk based algorithms take O(root N ln N) 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 O(root N ln N) steps, thus giving an O(root ln N) improvement over the known algorithms. The improvement is achieved by controlling the quantum walk on the lattice using an ancilla qubit.
|Item Type:||Journal Article|
|Additional Information:||Copyright belongs to The American Physical Society.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Physics|
|Date Deposited:||20 Jul 2009 11:46|
|Last Modified:||19 Sep 2010 04:54|
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