  Entanglement renormalization is a unitary real-space renormalization scheme.
The corresponding quantum circuits or tensor networks are known as MERA, and
they are particularly well-suited to describing quantum systems at criticality.
In this work we show how to construct Gaussian bosonic quantum circuits that
implement entanglement renormalization for ground states of arbitrary free
bosonic chains. The construction is based on wavelet theory, and the dispersion
relation of the Hamiltonian is translated into a filter design problem. We give
a general algorithm that approximately solves this design problem and provide
an approximation theory that relates the properties of the filters to the
accuracy of the corresponding quantum circuits. Finally, we explain how the
continuum limit (a free bosonic quantum field) emerges naturally from the
wavelet construction.
