Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator

TL;DR

This paper demonstrates that a continuous MERA (cMERA) circuit can represent a Chern insulator with nonzero topological properties and can be implemented on existing analog quantum computers, advancing quantum simulation techniques.

Contribution

It shows that cMERA can encode topologically nontrivial states and be realized in current analog quantum computing platforms, unlike discrete MERA.

Findings

cMERA fixed point wavefunction has nonzero Chern number

cMERA circuit can be implemented on ultracold atomic Fermi gases

Potential for efficient state preparation in analog quantum computers

Abstract

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.