Andrea MorelloIntroduction to quantum information in higher dimensions: high-spin nuclei in silicon and their analogy to other qudits*

The near-totality of quantum information science is based upon the use of qubits (quantum systems with dimensions d=2), of which a spin 1/2 is the simplest example. However, this is not the only option. Physical systems with d>2 ("qudits") allow to reduce the complexity of certain quantum circuits, and improve algorithmic efficiency. High dimensions are essential to accommodate error-corrected logical qubits. While traditional error correction schemes require a large number of physical qubits, it is also possible to encode a logical qubit in a single physical object with d>>2, as is becoming popular in bosonic (such as GKP) codes for microwave and optical systems.

Here I will present a new qudit platform, the spin 7/2 nucleus of an antimony atom in silicon [1]. Its 8-dimensional Hilbert space affords enough complexity to embody an error correctable logical qubit, hosted in a single atomic-scale platform. Together with the donor-bound spin 1/2 electron, it can form a 16-dimensional Hilbert space which can be controlled with both magnetic and electric fields [2]. Experiments are underway to demonstrate nonclassical states of the spin, such as Schroedinger cat states [3], as well as logical qubit encodings that exploit the symmetry and natural interactions in the physical Hamiltonian of the large nuclear spin [4].

This introductory talk will present a unified picture of the physics and quantum information aspects of qudits across different physical platforms, highlighting the universality of high-dimensional quantum information processing. I expect that the prospect of encoding a logical qubit in a single atomic-scale object, hosted in a silicon nanoelectronic device, will give further impetus to this broad line of research.

[1] S Asaad, V Mourik et al., Nature 579, 205 (2020)

[2] I Fernandez de Fuentes et al., arXiv:2306.07453 (2023)

[3] P Gupta et al. arXiv:2304.13813 (2023)

[4] J. Gross, Phys. Rev. Lett. 127, 010504 (2021)