Entanglement Hamiltonian tomography in quantum simulation

By C. Kokail, R. van Bijnen, Andreas Elben, B. Vermersch, Peter Zoller. Nature Physics, 2020

139 citations recorded by the source corpus.

Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in the closed-system dynamics of quantum simulators remains a 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 quasilocal few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomized measurements. By analysing data from trapped-ion quantum simulators for quench dynamics of a one-dimensional long-range Ising model, we demonstrate the ability of the protocol to measure the time evolution of the entanglement spectrum, in agreement with theoretical expectations. Furthermore, we develop the protocol as a testbed for predictions of entanglement structure in quantum field theories, which we illustrate for conformal field theory in quench dynamics, as well as the Bisognano–Wichmann theorem for ground states. In theoretical simulations, we demonstrate favourable scaling of sampling efficiency with subsystem size. Although the post-processing might ultimately be exponential, our protocol addresses the bottleneck of exponential sampling complexity in the investigation of entanglement structure in quantum simulation, and brings subsystems of tens of spins into reach for present experiments Entanglement is central to theories of quantum many-body systems but is very resource intensive to measure. A protocol based on a quasilocal parametrization of physical states allows entanglement structures to be studied using very few measurements.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bb30383816a2c977fadeaf1877a7f6f8cdbfeb37

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Citations in the corpus

Practical quantum advantage in quantum simulation (2022, methodology): “An exciting opportunity in the near term, however, is the potential for programmable quantum simulators that begin with the capabilities of an analogue system, and add the control from digital systems in different forms 97–102 .”
The randomized measurement toolbox (2022, methodology): “Another avenue for generalization is provided by learning the ‘entanglement Hamiltonian’ 95 .”
Quantum simulation of fundamental particles and forces (2023, background): “In general, access to the full final-state wavefunctions is not possible, but recently proposed techniques, such as classical shadows [111, 158–160], permits sampling of the density matrix and evaluation of observables with significant reductions in required resources.”