Applications of nonlinear interactions for quantum simulations and computing with motional modes of trapped ions

Thanks to its large accessible Hilbert space, using motional states of trapped ions for quantum simulations and quantum computing shows promise. However, such applications require implementing various forms of strong and well controlled nonlinear interactions between these normal modes of motion.

In particular, nonlinear coupling between the normal modes of motion can be achieved by exploiting the anharmonicity introduced via the Coulomb interaction between ions. We demonstrate some applications of such nonlinear coupling, including the realization of a small absorption refrigerator made up of 3 trapped ions. Additionally, coupling the spin and motion of the ions also gives rise to nonlinear interactions. Such interactions enable experimental implementation of a SWAP test, which measures the overlap between two infinitely-dimensional quantum states of harmonic oscillators. By utilizing the SWAP test, we carry out simple machine learning algorithms that classify high-dimensional quantum states.