Donor molecules and nuclear spins: a resource for quantum computing

Abstract

In this thesis we investigate donor molecules as a resource for scaling-up donor-based spin qubits in silicon towards error-corrected quantum computers. We first propose a novel donor-based qubit consisting of an electron spin spread across a single donor (1P) and a two-donor molecule (2P) that is electrically driven and coupled utilising the hyperfine interaction. This qubit belongs to a class of electron spin qubits called “flopping-mode” qubits, where the electron wave function is spread over two quantum dots. Using a complete error model, we first investigate how to minimise errors and the electrical driving power in the general class of qubits by optimising the magnetic gradients across the device. We then demonstrate how the magnetic gradient on the new qubit design can be atomically engineered using the hyperfine interaction within the donor molecules. In particular we show that by controlling the orientation of the nuclear spins in the qubit we can suppress the deleterious magnetic gradient originating from the hyperfine interaction within the two-donor molecule. We predict qubit errors well below 10−3 and show that the 1P-2P flopping-mode qubit can be strongly coupled to a superconducting cavity. Finally, we outline a way to scale the proposed qubits to a larger cavity-based architecture.

Following this theoretical proposal we present experimental evidence that the required engineering of 2P donor-molecules is possible, using two atomic precision devices fabricated with hydrogen-resist STM lithography. We achieve high accuracy precision patterning of two different devices that contain donor molecules to reveal the following results. First we show how to improve the fidelity of single shot electron spin readout from 83% to 94% using an optimised SET design. ESR spectra performed using adiabatic spin inversion yield precise measurements of the hyperfine interactions within the molecule. Using atomistic tight binding calculations in collaboration with the group of Professor Rahman we were able to perform metrology of the individual donor configurations within the dots. The metrology could be performed with a precision of ±0.25nm using measurements of the charging energies and improved to atomic precision using the hyperfine spectroscopy. The ESR spectra demonstrated the first observation of a Stark shift in a tightly bound donor molecule. The magnitude of the shift observed was shown to depend on the molecular orientation within the crystal and offers future strategies for hyperfine engineering for optimal qubit operation. Finally, we demonstrate the first nuclear-spin readout of a tightly-bound donor molecule, with a fidelity of 88%, and show how we can track the nuclear spin states over time. Using a hidden Markov model we extracted the nuclear transition frequencies and uncover possible evidence of a dipolar coupling between the nuclear spins.