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AIP conference proceedings

Robustness of the quantum search algorithm

B. Pablo-Norman, M. Ruiz-Altaba

Published Jan 1, 1999• 0 citations
Publisher

Abstract

We find exact results for Grover's quantum search algorithm and analyze its behavior under noisy situations when no quantum correction codes are available.We compute how the algorithm slows down: it is still better than a classical one, provided the noise is smaller than some bound, which we also compute.
DOI
10.1063/1.1301410

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Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modeled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustess when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as ${N}^{\ensuremath{-}2/3}.$
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We investigate the problem of quantum searching on a noisy quantum computer. Taking a fault-ignorant approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Groverʼs algorithm) still outperform the best noiseless classical search algorithm.
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