Entanglement Renormalization Circuits for Chiral Topological Order

Understand

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.