Fig. 4: STIRAP process for the two-qubit Controlled-Z (CZ) gate implementation.

a STIRAP pulse sequence, where the majority of population transfer occurs during the rising and dropping stages enclosed by the “square” pulse shape. Here we only plot the absolute values of both driving amplitudes, see Supplementary Information for more details. b Population and phase evolution when only one spin is coupled to the STIRAP process. Phonon is pumped to its first excited state and then transferred back again, which preserves the \(\left\vert {g}_{2}{g}_{3}\right\rangle\) and \(\left\vert {g}_{3}{g}_{2}\right\rangle\) states. c Population and phase evolution when two spins are coupled to the STIRAP process simultaneously. Phonon is pumped to its second excited state and then transferred back again, yielding a γ₂ − 2γ₁ = π phase difference for the \(\left\vert {g}_{2}{g}_{2}\right\rangle\) input state compared to the single spin scenario. d Full quantum process tomography for the CZ gate demonstrated by the real part of the χ matrix, featuring a gate fidelity of 96.80%. e Demonstration of the feasibility of the gate protocol with some non-ideal system parameters (e.g., the spin dephasing here), over 90% gate fidelity, is still achievable with spin coherence time down to 100 μs.