Simulating the Morse potential with a pair of oscillators using circuit QED

Hybrid continuous-variable discrete-variable (CV-DV) systems implemented with 3D circuit QED (cQED) are a promising platform for quantum simulations of chemistry, with degrees of freedom in such problems better encoded on bosonic hardware than with qubits alone. Linear vibrations can be encoded in a single oscillator and rotational degrees of freedom can be encoded in two oscillators with the Schwinger boson method. This method can also be used to encode the anharmonic Morse potential by encoding vibrational degrees of freedom into pairs of bosonic modes. In this representation, the vibronic Hamiltonian manifests as nonlinear pair-beamsplitter interactions between two oscillator modes. We explore digital experimental implementations of such nonlinear interactions through quantum signal processing (QSP) as well as analog implementations using sideband Raman transitions. We also present methods for measuring the desired vibrational observables, which are non-linear functions of the oscillator ladder operators. We will report on our experimental progress on implementing this in a two-mode cQED system.