Experimental implementation of a Raman-assisted six-quanta process

Fault tolerant quantum information processing requires specific nonlinear interactions acting within the Hilbert space of the physical system that implements a logical qubit. The required order of nonlinearity is often not directly available in the natural interactions of the system. Here, we experimentally demonstrate a route to obtain higher-order nonlinearities by combining more easily available lower-order nonlinear processes, using a generalization of the Raman transitions. In particular, we demonstrate a Raman-assisted transformation of four photons of a high-Q superconducting cavity into two excitations of a superconducting transmon mode and vice versa. The resulting six-quanta process is obtained by cascading two fourth-order nonlinear processes through a virtual state. This process is a key step towards hardware efficient quantum error correction using Schrödinger cat-states.