Quantum optical systems with cold atoms an ions provides one of the best ways to build controllable quantum many-body systems as quantum computers and quantum simulators. Here we report on recent developments in building, and in particular programming quantum computers and quantum simulators based on trapped ions as intermediate scale quantum devices. We address, and illustrate this for a range of applications from solving the quantum many-body problem, to developing and implementing novel measurement protocols for many-body observables, and questions of verification and validation of quantum devices. Examples highlighting these developments include quantum simulation of the Lattice Schwinger Model, as a toy model of 1D QED and Lattice Gauge Theory. We first demonstrate `digital’ quantum simulation of Schwinger evolution on a small scale quantum computer, and we discuss implementation of self-verifying `variational’ quantum simulations on a programmable quantum simulator, which we illustrate by computing the ground state and quantum phase transition of the Schwinger Model. In addition, we discuss quantum protocols and classical post-processing, which allow us to access in equilibrium and non-equilibrium dynamics quantities like entanglement entropies and the entanglement spectrum.
Wolfgang Lerche / TH-SP