@article {1377, title = {Fast quantum algorithm for numerical gradient estimation}, journal = {Physical Review Letters}, volume = {95}, year = {2005}, month = {2005/7/28}, abstract = { 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. }, doi = {10.1103/PhysRevLett.95.050501}, url = {http://arxiv.org/abs/quant-ph/0405146v2}, author = {Stephen P. Jordan} }