Tomography of universal two-qubit logic operations in exchange-coupled donor electron spin qubits*

Scalable quantum processors require high-fidelity universal quantum logic operations, in a manufacturable physical platform. The spin of an electron bound to a single donor atom in silicon has shown coherence times of almost a second, with single qubit quantum operation fidelities of over 99.9%. Here we present the experimental demonstration and tomography of universal 1- and 2-qubit gates in a system of two weakly exchange-coupled electrons, with each electron bound to a single donor phosphorus nucleus. By deterministically preparing the two nuclear spins in opposite directions, each electron spin resonance pulse constitutes a native conditional two-qubit gate.  We carefully benchmark the fidelity of these native operations using the technique of gate set tomography (GST), achieving qubit gate fidelities above 99% for both electrons separately. We show that, as a result of working in the weak exchange regime, this coupling mechanism has negligible effect on qubit coherence. The GST method provides precious insights into the nature of the residual errors, and informs strategies for further improvement.