White Noise in Quantum Random Walk Search Algorithm

The quantum random walk is a possible approach to construct new quantum search algorithms. It has been shown by Shenvi et al. Phys. Rev. A 67(2003)52307 that a kind of algorithm can perform an oracle search on a database of N items with O(√N) calling to the oracle, yielding a speedup similar to other quantum search algorithms. We study the effect of white or Gaussian noise on this algorithm. The algorithm loses efficiency when noise is added. We also show that noise on the target state plays a more important role than that on other states. Finally we compare the effects of similar types of noise in the quantum random walk search algorithm and Grover's search algorithm.