Riemannian geometry of quantum computation

A review is given of some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group, SU(2n)SU(2n). Using the Lie algebra su(2n)su(2n), detailed derivations are given of a useful Riemannian geometry of SU(2n)SU(2n), including the connection and the geodesic equation for minimal complexity quantum computations.