Rick van Bijnen

Guest Speaker: Professor Rick van Bijnen
Affiliation: Institut für Quantenoptik und Quanteninformation
Location: Virtual meeting on Zoom (Instructions below)
Date: Dec 10, 2020
Time: 1:00 PM Eastern time

"Entanglement Hamiltonian Tomography in Quantum Simulation"
Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum devices. Here we discuss an efficient tomographic protocol for reconstructing reduced density matrices and entanglement spectra for spin systems. The key step is a parametrization of the reduced density matrix in terms of an entanglement Hamiltonian involving only quasi local few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomised measurements. The ansatz is suggested by Conformal Field Theory in quench dynamics, and via the Bisognano-Wichmann theorem for ground states. Not only does the protocol provide a testbed for these theories in quantum simulators, it is also applicable outside these regimes. We show the validity and efficiency of the protocol for a long-range Ising model in 1D using numerical simulations. Furthermore, by analyzing data from 10 and 20 ion quantum simulators, we demonstrate measurement of the evolution of the entanglement spectrum in quench dynamics.