Fig. 1: S−T0 qubit energy diagram and Bloch sphere.

The eigenenergies change as a function of detuning ϵ, which is used to control the exchange coupling J(ϵ). The ϵ pulses presented in this work start and finish at a baseline \({\epsilon }_{\min }\) with low J and pulse to higher values for short periods. The maximum amplitude is constrained to below the S−T+ anticrossing at large ϵ. We choose the convention that J(ϵ) points along the y-axis of the Bloch sphere. For low ϵ amplitudes, the qubit rotates about ΔBz, the z-axis of the Bloch sphere. Large amplitude ϵ pulses rotate the qubit about the y-axis and thus enable arbitrary single-qubit gates.