Quantum Variational Learning of the Entanglement Hamiltonian

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.

Automated summary

This study describes a protocol for learning the structure of the entanglement Hamiltonian by deforming the many body Hamiltonian physically realized on a quantum device. Optimal variational parameters are determined through a feedback loop involving quench dynamics and classical optimization, resulting in excellent agreement of the EH with Bisognano-Wichmann predictions in the ground state of Fermi-Hubbard models. Subsequent on-device spectroscopy allows for a direct measurement of the entanglement spectrum.