Hybrid Quantum-Classical QAOA Quantum Simulation with Trapped Atomic Ions*

Hybrid quantum-classical algorithms, such as quantum approximate optimization algorithms (QAOA)\footnote{E. Farhi et al., arXiv:1411.4028v1}, are a promising tool to provide an approximate set of solutions to combinatorial optimization problems and to prepare non-trivial quantum states\footnote{W. W. Ho \& T. H. Hsieh, arXiv:1803.00026v3}. Here we report the implementation of a shallow-depth QAOA protocol with trapped atomic ions to compute the ground state energy of the transverse field Ising model with tunable long-range interactions. We performed an exhaustive search of the variational parameters to optimize the algorithm and investigated its performance as a function of system size. We plan to interface our quantum simulator with a classical optimization algorithm to find a set of parameters that minimize the energy output of QAOA.