High-fidelity qutrit entangling gates with superconducting circuits based on parametric coupling

Recently, significant progress has been made in the demonstration of single qutrit and coupled qutrit gates with superconducting circuits. Coupled qutrit gates have significantly lower fidelity than single qutrit gates, owing to long implementation times. We present a protocol to implement CZ gates using two fixed frequency transmons capacitively coupled to a tunable transmon. We make use of fundamental gates that are iSWAP-like exchanges between the two qutrit states |01> to |10> and the states |12> to |21>. Parametric coupling is used to conduct these exchanges by driving an AC flux in the tunable coupler of an appropriate frequency which is different for the two kinds of exchanges. We show that these gates have high expressibility when combined with single qutrit rotations. We show that a high-fidelity CZ gate can be obtained by combining these entangling gates with single qutrit rotations.