Su-Kuan Chu

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).

Quantum simulation of fermionic systems is a leading application of quantum computers. One promising approach is to represent fermions with qubits via fermion-to-qubit mappings. In this work, we present high-distance fermion-to-qubit stabilizer codes for simulating 2D and 3D fermionic systems. These codes achieve arbitrarily large code distances while keeping stabilizer weights constant. They also preserve locality by mapping local fermionic operators to local qubit operators at any fixed distance. Notably, our 3D construction is the first to simultaneously achieve high distance, constant stabilizer weights, and locality preservation. Our construction is based on concatenating a small-distance 2D or 3D fermion-to-qubit code with a high-distance fermionic color code. Together, these features provide a robust and scalable pathway to quantum simulation of fermionic systems.