Quantum Variational Learning of the Entanglement Hamiltonian

The experimental capabilities of quantum simulation platforms, such as ultracold atoms, Rydberg tweezer arrays and trapped ions, already allow to realise and probe a variety of model Hamiltonians. However, the development of efficient and scalable protocols to measure the entanglement properties of quantum many-body systems - as encoded in the Entanglement Hamiltonian (EH) and its eigenvalues, the Entanglement spectrum (ES) - remains an outstanding challenge.

In this talk, I will present recent progress towards learning the EH in quantum simulations using a variational quantum-classical hybrid algorithm. Our protocol is enabled by the approximate locality of the EH, which is motivated by the Bisognano-Wichmann theorem of quantum field theory. For the example of a Fermi-Hubbard model on a ladder geometry our results demonstrate the experimental feasibility of the proposed algorithm. I will further discuss the application of such protocols to topological states, where it will allow to test with existing quantum simulators the Li-Haldane conjecture that the low-lying ES is related to the conformal field theory of edge excitations.