  We introduce a unified formulation of variational methods for simulating
ground state properties of quantum many-body systems. The key feature is a
novel variational method over quantum circuits via infinitesimal unitary
transformations, inspired by flow equation methods. Variational classes are
represented as efficiently contractible unitary networks, including the
matrix-product states of density matrix renormalization, multiscale
entanglement renormalization (MERA) states, weighted graph states, and quantum
cellular automata. In particular, this provides a tool for varying over classes
of states, such as MERA, for which so far no efficient way of variation has
been known. The scheme is flexible when it comes to hybridizing methods or
formulating new ones. We demonstrate the functioning by numerical
implementations of MERA, matrix-product states, and a new variational set on
benchmarks.
