  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.
