  Motivated by recent studies of holographic complexity, we examine the
question of circuit complexity in quantum field theory. We provide a quantum
circuit model for the preparation of Gaussian states, in particular the ground
state, in a free scalar field theory for general dimensions. Applying the
geometric approach of Nielsen to this quantum circuit model, the complexity of
the state becomes the length of the shortest geodesic in the space of circuits.
We compare the complexity of the ground state of the free scalar field to the
analogous results from holographic complexity, and find some surprising
similarities.
