Implementation of a generalized controlled-NOT gate between fixed-frequency transmons

Abstract

We have embedded two fixed-frequency Al/AlO$_{\textrm{x}}$/Al transmons, with ground-to-excited transition frequencies at 6.0714 GHz and 6.7543 GHz, in a single 3D Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a -1 MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (Speeding up Waveforms by Inducing Phases to Harmful Transitions) technique, we demonstrate the operation of a generalized controlled-not (CNOT) gate between the two qubits, with a gate time $\tau_g= 907$ ns optimized for this device. Using quantum process tomography we find that the gate fidelity is 83%-84%, somewhat less than the 87% fidelity expected from relaxation and dephasing in the transmons during the gate time.