Readout Protocol for High-Spin donor nuclei integrated with quantum dots

High-spin donor nuclei in silicon are an emerging platform for encoding quantum information in high-dimensional qudits. The generation and manipulation of Schrödinger cat states in spin-7/2 antimony atoms illustrates the potential for encoding logical qubits within a physical qudit [1]. However, using such a system for repetitive quantum error correction remains a significant challenge. Standard readout methods, which rely on rotating a hyperfine-coupled electron conditioned on the nuclear spin state and then reading the electron by spin-dependent tunneling [2], randomize the phase of all nuclear states.

Here we propose two new readout protocols for high-spin nuclear qudits, based on integrating the donor with lithographic quantum dots. The coupled donor-dot system allows us to readout the nuclear spin via intermediate electron spins on quantum dots. By coupling the dot electron to the donor-bounded electron via exchange interaction, we reduce the measurement back-action on the nuclear qudit, such that the readout-induced phase error becomes correctable. Our simulation results demonstrate that, with the application of dynamical decoupling techniques, phase errors caused by tuning the exchange coupling and electron flips can be effectively corrected.

[1] Yu, X., Wilhelm, B., Holmes, D., Vaartjes, A., Schwienbacher, D., Nurizzo, M., Kringhøj, A., van Blankenstein, M.R., Jakob, A.M., Gupta, P. and Hudson, F.E., 2024. Creation and manipulation of Schrödinger cat states of a nuclear spin qudit in silicon. arXiv preprint arXiv:2405.15494.

[2] Fernández de Fuentes, I., Botzem, T., Johnson, M.A., Vaartjes, A., Asaad, S., Mourik, V., Hudson, F.E., Itoh, K.M., Johnson, B.C., Jakob, A.M. and McCallum, J.C., 2024. Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields. Nature communications, 15(1), p.1380.