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Effects of Noisy Oracle on Search Algorithm Complexity

Neil Shenvi·Kenneth R. Brown·K. Birgitta Whaley
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Abstract

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.

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Neil Shenvi, Kenneth R. Brown, K. Birgitta Whaley. 2003-12-09. Effects of Noisy Oracle on Search Algorithm Complexity. https://doi.org/10.1103/physreva.68.052313

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