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).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).

arXiv:2304.13748Apr 26, 20231 citation

Thermal Multi-scale Entanglement Renormalization Ansatz for Variational Gibbs State Preparation

Troy J. Sewell, White, Christopher David, Brian G. Swingle

Many simulation tasks require that one first prepare a system's Gibbs state. We present a family of quantum circuits for variational preparation of thermal Gibbs states on a quantum computer; we call them the thermal multi-scale entanglement renormalization ansatz (TMERA). TMERA circuits transform input qubits to wavepacket modes localized to varying length scales and approximate a systems Gibbs state as a mixed state of these modes. The TMERA is a based on the deep multi-scale entanglement renormalization ansatz (DMERA); a TMERA modifies a ground-state DMERA circuit by preparing each input qubit as a mixed state. The excitation probabilities for input qubits serve as variational parameters used to target particular temperature Gibbs states. Since a TMERA is a special case of the product spectrum ansatz for thermal states, it is simple to prepare, analyze, and optimize. We benchmark the TMERA on the transverse field Ising model in one dimension and find that for $D=6$ it produces global fidelities $\mathcal F > 0.4$ for 512-site systems across all temperatures.Many simulation tasks require that one first prepare a system's Gibbs state. We present a family of quantum circuits for variational preparation of thermal Gibbs states on a quantum computer; we call them the thermal multi-scale entanglement renormalization ansatz (TMERA). TMERA circuits transform input qubits to wavepacket modes localized to varying length scales and approximate a systems Gibbs state as a mixed state of these modes. The TMERA is a based on the deep multi-scale entanglement renormalization ansatz (DMERA); a TMERA modifies a ground-state DMERA circuit by preparing each input qubit as a mixed state. The excitation probabilities for input qubits serve as variational parameters used to target particular temperature Gibbs states. Since a TMERA is a special case of the product spectrum ansatz for thermal states, it is simple to prepare, analyze, and optimize. We benchmark the TMERA on the transverse field Ising model in one dimension and find that for $D=6$ it produces global fidelities $\mathcal F > 0.4$ for 512-site systems across all temperatures.

arXiv:2210.16419Oct 28, 20224 citations

The entanglement structure of topological quantum phases

Michael Mariën

Jan 1, 20160 citations

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).

D=6

it produces global fidelities

\mathcal F > 0.4

for 512-site systems across all temperatures.