Extended Data Fig. 7: Qubit crosstalk and the SMART protocol.
From: High-fidelity spin qubit operation and algorithmic initialization above 1 K
a, Crosstalk due to off-resonance driving at B0 = 0.5 T and T = 1 K, plotted in time and frequency domain. In this measurement, ΔEZ and microwave power are set such that when Q1 is resonantly driven at fRabi, the Rabi frequency of the off-resonance driving on Q2 is exactly 4fRabi to meet the cancellation condition in equation (3), with N = 4. This also applies to the case where Q2 is resonantly driven and Q1 is off-resonantly driven. b, Single-qubit randomised benchmarking (RB) of Q1 with and without off-resonance driving at B0 = 0.5 T and T = 1 K. We maximise and cancel the off-resonance driving using the relationship in a. c, fRabi used in single-qubit RB at different B0. This is set to meet the off-resonance driving cancellation condition based on the ΔEZ in each B0 and charge configuration following equation (3). We use N = 4 for fast driving until we reach the limit of the microwave source at high B0, where the power transmission in the microwave line becomes much weaker. d, Sequence for probing the AC Stark shift and the results in time and frequency domain, taken at B0 = 0.5 T and T = 1 K. In this example, we use Q2 to probe the AC Stark shift: we prepare it in the -Y direction and apply a microwave pulse with varying frequency fMW and duration tMW. We show the results with and without correction. Without correction, AC Stark shift is seen as the linear fringes, which will translate into coherent Z errors during two-qubit operation. e, Sequence for the SMART dressing protocol8. The sequence prepares the target qubit along the +X axis, and drive it with a cosine-modulated microwave pulse for a duration of Tmodulation. The qubit is then projected back onto the +Z axis for measurement.