By employing a fully controlled cavity quantum electrodynamic system made of superconducting circuits, we experimentally create matrix product states, a class of states that has proven to be extremely powerful as a variational ansatz for numerical simulations. We create 1000 such quantum states and efficiently probe their correlation properties to determine an approximation to the ground state of a model describing a gas of interacting quantum particles. Having physical access to the simulated ground-state wave functions enables us to also probe higher-order correlation functions beyond measuring the ground-state energy. The experimental data are in good agreement with the exact solution over a wide range of interaction strengths of the model.