Fast Quantum Algorithm for Numerical Gradient Estimation

S. P. Jordan, "Fast Quantum Algorithm for Numerical Gradient Estimation"
PRL 95, 050501 (2005)

Gradient evaluation is an important subroutine in a wide variety of problems in quantum chemistry and nanoscience (not to mention many other "real world" problems. Classically, for a d-dimensional system, at least d+1 function calls are required in order to determine the gradient; Jordan demonstrates a quantum algorithm that can do this in only one function call, using a generalization of the Bernstein-Vazirani algorithm to continuous functions with finite precision. Now we only need to build a quantum computer...