Quantum Variational Learning of the Entanglement Hamiltonian

TL;DR

This paper introduces a variational protocol using quantum devices to learn the entanglement Hamiltonian of many-body states, validated through simulations of Fermi-Hubbard models and on-device spectroscopy.

Contribution

It proposes a novel variational method employing spatial deformations and feedback loops to efficiently determine the entanglement Hamiltonian on quantum hardware.

Findings

Excellent agreement with Bisognano-Wichmann predictions for EH.

Successful on-device spectroscopy of entanglement spectrum.

Applicable to topological phases in Fermi-Hubbard models.

Abstract

Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.