Fig. 1: Two-qubit gates and quantum coherence of silicon spin qubits operated at a T = 1.05 K.

a Schematic representation of the double quantum dot system. The device is the same as used in ref. ¹⁹. Two plunger gates (P₁ and P₂) and one barrier gate (B_t) are used to control the detuning energy ϵ and the tunnel coupling t between the quantum dots. Spin manipulation occurs via electron-spin-resonance (ESR) using an on-chip microwave line. The energy diagram displays the four electron spin states as a function of ϵ. We exploit both driven rotations and pulsed exchange for coherent control. Controlled rotations (CROTs) can in principle be executed at all points where J ≠ 0, given that gate times are appropriately set. CPHASE gates are conveniently executed when the exchange interaction is much smaller than the Zeeman energy difference between the qubits, while SWAP oscillations can be realized when the exchange interaction is much larger. b Using ESR control we find the four resonance frequencies of the two-qubit system. Here, the exchange interaction is tuned to 3 MHz. The spectrum is composed of the frequencies: f₁ (\(\left|\uparrow \downarrow \right\rangle \longrightarrow \left|\downarrow \downarrow \right\rangle\)), f₂ (\(\left|\downarrow \downarrow \right\rangle \longrightarrow \left|\downarrow \uparrow \right\rangle\)), f₃ (\(\left|\uparrow \uparrow \right\rangle \longrightarrow \left|\downarrow \uparrow \right\rangle\)) and f₄ (\(\left|\uparrow \downarrow \right\rangle \longrightarrow \left|\uparrow \uparrow \right\rangle\)). c Coherence times as a function of the number of refocusing π pulses. Here, the exchange is set to 2 MHz. The plot includes the dephasing times measured through a Ramsey experiment to allow comparison. d, e Realization of CROT operations. Rabi oscillations of the target qubit are controlled by the spin state of the control qubit. We find controlled rotations on all the four resonance frequencies f₁, f₂, f₃, f₄.