  The multi-scale entanglement renormalization ansatz (MERA) postulates the
existence of quantum circuits that renormalize entanglement in real space at
different length scales. Chern insulators, however, cannot have scale-invariant
discrete MERA circuits with finite bond dimension. In this Letter, we show that
the continuous MERA (cMERA), a modified version of MERA adapted for field
theories, possesses a fixed point wavefunction with nonzero Chern number.
Additionally, it is well known that reversed MERA circuits can be used to
prepare quantum states efficiently in time that scales logarithmically with the
size of the system. However, state preparation via MERA typically requires the
advent of a full-fledged universal quantum computer. In this Letter, we
demonstrate that our cMERA circuit can potentially be realized in existing
analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical
lattice with light-induced spin-orbit coupling.
