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We study the influence of errors and decoherence on both the performance ofShor's factoring algorithm and Grover's search algorithm, and on the amount ofinterference in these algorithms using a recently proposed interferencemeasure. We consider systematic unitary errors, random unitary errors, anddecoherence processes. We show that unitary errors which destroy theinterference destroy the efficiency of the algorithm, too. However, unitaryerrors may also create useless additional interference. In such a case thetotal amount of interference can increase, while the efficiency of the quantumcomputation decreases. For decoherence due to phase flip errors, interferenceis destroyed for small error probabilities, and converted into destructiveinterference for error probabilities approaching one, leading to successprobabilities which can even drop below the classical value. Our results showthat in general interference is necessary in order for a quantum algorithm tooutperform classical computation, but large amounts of interference are notsufficient and can even lead to destructive interference with worse thanclassical success rates.

Interference versus success probability in quantum algorithms with imperfections