An Adaptive, Fixed-Point Version of Grover's Algorithm

Abstract

We give an adaptive, fixed-point version of Grover's algorithm. By this we mean that our algorithm performs an infinite sequence of gradually diminishing steps (so we say it's adaptive) that drives the starting state to the target state with absolute certainty (so we say it's a fixed-point algorithm). Our algorithm is motivated by Bloch sphere geometry. We include with the ArXiv distribution of this paper some simple software (Octave/Matlab m-files) that implements, tests and illustrates some of the results of this paper.