  We present a modification of Simon's algorithm that in some cases is able to
fit experimentally obtained data to appropriately chosen trial functions with
high probability. Modulo constants pertaining to the reliability and
probability of success of the algorithm, the algorithm runs using only
O(polylog(|Y|)) queries to the quantum database and O(polylog(|X|,|Y|))
elementary quantum gates where |X| is the size of the experimental data set and
|Y| is the size of the parameter space.We discuss heuristics for good
performance, analyze the performance of the algorithm in the case of linear
regression, both one-dimensional and multidimensional, and outline the
algorithm's limitations.
