Donor spins in silicon have achieved record values of coherence times and single-qubit gate
fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic
gates, where the most natural coupling is the exchange interaction. To aid the efficient design of
scalable donor-based quantum processors, we model the two-electron wave function using a full
configuration interaction method within a multi-valley effective mass theory. We exploit the high
computational efficiency of our code to investigate the exchange interaction, valley population,
and electron densities for two phosphorus donors in a wide range of lattice positions, orientations,
and as a function of applied electric fields. The outcomes are visualized with interactive images
where donor positions can be swept while watching the valley and orbital components evolve
accordingly. Our results provide a physically intuitive and quantitatively accurate understanding of
the placement and tuning criteria necessary to achieve high-fidelity two-qubit gates with donors in
silicon.

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