摘要：We give a multidimensional version of amplitude estimation. Let p be an n-dimensional probability distribution which can be sampled from using a quantum circuit U_p. We show that all coordinates of p can be estimated up to error ε per coordinate using Ã.(1/(ε)) applications of U_p and its inverse. This generalizes the normal amplitude estimation algorithm, which solves the problem for n = 2. Our results also imply a Ã.(n/ε) query algorithm for ð"â,-norm (the total variation distance) estimation and a Ã.(â^Sn/ε) query algorithm for ð"â,,-norm. We also show that these results are optimal up to logarithmic factors.
关键词：quantum algorithms; amplitude estimation; monte carlo
