(2).Using mn copies of p we obtain m copies of the decomposition (2),where the ith eigenvalue r;appearsrim times.The features of the ith eigenstate can then be determined by performing a quan- tum measurement to obtain the expectation value(xMIX)of the eigenvector with eigenvalue r for desired Hermitian M.As long as M is sparse-14 or efficiently simulable by the methods given in this paper,this measurement can itself be performed in time O(logd)