Kerr- and cross-Kerr-free Josephson four-wave mixing device*

Parametrically pumped four-wave mixing is a key building block for many developments in the field of superconducting quantum information processing. However, undesired frequency shifts such as Kerr, cross-Kerr and Stark shifts, inherent with four-wave mixing, lead to difficulties in tuning up the desired parametric processes and, for certain applications, severely limit the fidelities of the resulting operations. In this talk, we explore a Josephson four-wave mixing device consisting of a SQUID transmon coupled to a half-flux biased SNAIL transmon, a.k.a. capacitively shunted flux qubit. When the two transmons have matching frequencies, an interference effect cancels the negative Kerr of the SQUID transmon with the positive Kerr of the SNAIL transmon while preserving parametric four-wave mixing capabilities. We present the design and experimental characterization of such a device.