  Entanglement renormalization circuits are quantum circuits that can be used
to prepare large-scale entangled states. For years, it has remained a mystery
whether there exist scale-invariant entanglement renormalization circuits for
chiral topological order. In this paper, we solve this problem by demonstrating
entanglement renormalization circuits for a wide class of chiral topologically
ordered states, including a state sharing the same topological properties as
Laughlin's bosonic fractional quantum Hall state at filling fraction $1/4$ and
eight states with Ising-like non-Abelian fusion rules. The key idea is to build
entanglement renormalization circuits by interleaving the conventional
multi-scale entanglement renormalization ansatz (MERA) circuit (made of
spatially local gates) with quasi-local evolution. Given the miraculous power
of this circuit to prepare a wide range of chiral topologically ordered states,
we refer to these circuits as MERA with quasi-local evolution (MERAQLE).
