Entanglement Renormalization Circuits for Chiral Topological Order

• URL: http://arxiv.org/abs/2304.13748v1
• Date: Wed, 26 Apr 2023 18:00:02 GMT
• Title: Entanglement Renormalization Circuits for Chiral Topological Order
• Authors: Su-Kuan Chu, Guanyu Zhu, and Alexey V. Gorshkov
• Abstract summary: Entanglement renormalization circuits are quantum circuits that can be used to prepare large-scale entangled states. We build entanglement renormalization circuits by interleaving the conventional multi-scale entanglement renormalization ansatz with quasi-local evolution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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).

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