@MISC{Mosca00quantumamplitude, author = {Michele Mosca}, title = {Quantum Amplitude Amplification and Estimation}, year = {2000} }

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Abstract

Abstract Consider a Boolean function O / : X! f0; 1g that partitions set X between its good and bad elements, where x is good if O/(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that Aj0i = P x2X ffxjxi is a quantum superposition of the elements of X, and let a denote the probability that a good element is produced if Aj0i is measured. If we repeat the process of running A, measuring the output, and using O / to check the validity of the result, we shall expect to repeat 1=a times on the average before a solution is found. Amplitude amplification is a process that allows to find a good x after an expected number of applications of A and its inverse which is proportional to 1= p a, assuming algorithm A makes no measurements.