Extended Data Fig. 6: Preparation of quadruple quantum dot state.

a, Verification of exchange oscillations on the left side. Initializing the left side in the \(\left|\uparrow \uparrow \right\rangle \) state before a T₁₂ pulse yields no exchange oscillations. Initialization in the \(\left|\downarrow \uparrow \right\rangle \) state shows exchange oscillations. b, Initializing the right side in the \(\left|\uparrow \uparrow \right\rangle \) state before a T₃₄ pulse yields no exchange oscillations. Initialization in the \(\left|\downarrow \uparrow \right\rangle \) state shows exchange oscillations. c, Verification of the ground-state orientation of the right side. We load the left side in the \(\left|\uparrow \uparrow \right\rangle \) state and the right side by adiabatic separation of the singlet state, which gives either \(\left|\uparrow \downarrow \right\rangle \) or \(\left|\downarrow \uparrow \right\rangle \), depending on the sign of the gradient. We pulse T₂₃ to induce exchange between the middle two spins. Dynamic nuclear polarization with singlets yields no oscillations, whereas pumping with triplets yields oscillations. These data confirm that the separated singlet state evolves to the \(\left|\downarrow \uparrow \right\rangle \) state under triplet pumping for the right side. d, Verification of the ground state of the left side. We initialize the array by separating singlets on both sides. In the case of triplet pumping on the right side, the third spin is \(\left|\downarrow \right\rangle \), so the second spin must be \(\left|\uparrow \right\rangle \) in order to generate exchange oscillations with a T₂₃ pulse, as measured on the left side. Singlet pumping on the left side yields no exchange oscillations. e, The same initialization and pulses as in e, but measured on the right side. In all cases, \({P}_{{\rm{S}}}^{{\rm{L}}\left({\rm{R}}\right)}\) indicates the singlet return probability measured on the left (right) side.