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 [1], with single qubit quantum operation fidelities of over 99.9% [2]. 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 [3]. 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. Adding to the recent demonstration of universal 2-qubit gates for nuclear spins, and electron-nuclear entanglement [4], these electron two-qubit gates complete the toolbox for constructing a scalable spin-based quantum processor in silicon.<br/>[1] Muhonen, J. T. et al. <i>Storing quantum information for 30 seconds in a nanoelectronic device</i>. Nature nanotechnology 9, 986 (2014).<br/>[2] Dehollain, J. P. et al. <i>Optimization of a solid-state electron spin qubit using gate set tomography</i>. New Journal of Physics 18, 103018 (2016).<br/>[3] Madzik, M. T. et al. <i>Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device.</i> Nature Communications 12, 181 (2021).<br/>[4] Madzik, M. T. et al. <i>Precision tomography of a three-qubit electron-nuclear quantum processor in silicon.</i> arXiv:2106.03082 (2021)