Fast quantum algorithm for numerical gradient estimation

Given a blackbox for f, a smooth real scalar function of d real variables,
one wants to estimate the gradient of f at a given point with n bits of
precision. On a classical computer this requires a minimum of d+1 blackbox
queries, whereas on a quantum computer it requires only one query regardless of
d. The number of bits of precision to which f must be evaluated matches the
classical requirement in the limit of large n.