Thesis presented November 22, 2018

Abstract:
In the race for quantum computing, silicon has become a material of choice for the implementation of spin qubits. Such devices are fabricated in CEA using CMOS technologies, in order to facilitate their large-scale integration. This thesis covers the modeling of these qubits and in particular the manipulation of the spin state with an electric field. To that end, we use a set of advanced numerical tools to compute the potential and electronic structure in the qubits (in particular tight-binding and k.p methods), in order to be as close as possible to the experimental devices. These simulations allowed us to understand two important experimental results: on one hand the observation of the electrical manipulation of an electron spin, and on the other hand the characterization of the anisotropy of the Rabi frequency of a hole spin qubit.
The former result was rather unexpected, since the spin-orbit coupling is very low in the conduction band of silicon. We develop a model, confirmed by the simulations and some experimental results, that highlights the essential role of the intervalley spin-orbit coupling, enhanced by the low symmetry of the system. We use these results to propose and test numerically a scheme for the electrical manipulation of the qubit which consists in switching reversibly between a spin qubit and a valley qubit. Concerning the hole qubits, the relatively large spin-orbit coupling allows for fast electrical spin manipulation. However the experimental measurements of the Rabi frequency anisotropy show a complex physics, insufficiently described by the usual models. Therefore we develop a formalism that allows to model simply the Rabi frequency as a function of the magnetic field, and that can be applied to other types of spin-orbit qubits. The simulations reproduce the experimental features, and underline the important role of strain.

Keywords:
qubit, Quantum information, Quantum bits, Silicon Quantum Bits

On-line thesis.