Evaluating Robust Entanglement on a Trapped Ion Platform

We present proof of principle results for evaluating an entanglement volumetric benchmark [1] on trapped ion platforms. The benchmark quantifies the robustness of multipartite and bipartite entanglement using stabilizer measurements and witness functions. Each n-qubit graph state is prepared and used to evaluate $n$ state-specific stabilizer strings. These stabilizer measurements are used to evaluate entanglement witness functions. The entanglement benchmark defines families of graph states associated with an initial sub-graph of the hardware qubit connectivity - with all-to-all connectivity, trapped ion systems provide a flexibility in the choice of this initial graph, and this will affect the associated family. In this work, we present results targeting several classes of entangled states: 1) 1-D cluster states, 2) n-qubit GHZ states, and 3) cycle graph states. These states have been found in the literature as standard hardware benchmarks, and have connections to many near-term applications.