  The multiscale entanglement renormalization ansatz describes quantum
many-body states by a hierarchical entanglement structure organized by length
scale. Numerically, it has been demonstrated to capture critical lattice models
and the data of the corresponding conformal field theories with high accuracy.
However, a rigorous understanding of its success and precise relation to the
continuum is still lacking. To address this challenge, we provide an explicit
construction of entanglement-renormalization quantum circuits that rigorously
approximate correlation functions of the massless Dirac conformal field theory.
We directly target the continuum theory: discreteness is introduced by our
choice of how to probe the system, not by any underlying short-distance lattice
regulator. To achieve this, we use multiresolution analysis from wavelet theory
to obtain an approximation scheme and to implement entanglement renormalization
in a natural way. This could be a starting point for constructing quantum
circuit approximations for more general conformal field theories.
