Experimental realization of a nonlinear 3-wave mixing gate for quantum simulation

The ability to simulate an arbitrary Hamiltonian on a quantum device is an important step towards achieving universal quantum computing. We present a simulation of nonlinear 3-wave processes on a single qudit of the LLNL Quantum Design and Integration Testbed (QuDIT) resulting from iterative application of a gate developed to emulate these interactions. We describe our experimental protocol for realizing this simulation on the first three levels of a qudit and present results of average state population as a function of time. This experiment consists of a transmon-style qudit that is capacitively coupled to a superconducting 3D microwave cavity field. The qudit is addressed by a single-input RF signal that has been numerically optimized to perform 3-wave mixing unitary gate operations with fidelity of over 99%. We find that the average population of the qudit states evolve in a manner that matches the theoretically predicted quantum numbers of each wave in the 3-wave mixing process over many gate iterations.