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

TL;DR

This paper demonstrates control over a 16-dimensional quantum state space in a single antimony donor in silicon, using electric and magnetic fields, achieving high fidelity and revealing detailed system dynamics.

Contribution

It introduces a semiconductor platform with a high-spin donor qudit, enabling navigation of large Hilbert spaces with high fidelity, advancing quantum information processing capabilities.

Findings

Achieved gate fidelity >99.8% on nuclear spin

Controlled a 16-dimensional Hilbert space using electric and magnetic fields

Unveiled detailed system Hamiltonian and noise susceptibility

Abstract

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.