Navigating the 16-dimensional Hilbert space of a high-spin donor qudit using magnetic and electric fields

Efficient scaling and flexible control are key aspects of useful quantum
computing hardware. Spins in semiconductors combine quantum information
processing with electrons, holes or nuclei, control with electric or
magnetic fields, and scalable coupling via exchange or dipole interaction.
However, accessing large Hilbert space dimensions has remained
challenging, due to the short-distance nature of the interactions. Here,
we present an atom-based semiconductor platform where a 16-dimensional
Hilbert space is built by the combined electron-nuclear states of a single
antimony donor in silicon. We demonstrate the ability to navigate this
large Hilbert space using both electric and magnetic fields, with gate
fidelity exceeding 99.8\% on the nuclear spin, and unveil fine details of
the system Hamiltonian and its susceptibility to control and noise fields.
These results establish high-spin donors as a rich platform for practical
quantum information and to explore quantum foundations.