We discuss the modeling of the electrical manipulation of spin qubits in the linear-response regime where the Rabi frequency is proportional to the magnetic field and to the radio-frequency electric field excitation. We show that the Rabi frequency can be obtained from a generalized g-tensor magnetic resonance formula featuring a g-matrix and its derivative g with respect to the electric field (or gate voltage) as inputs. These matrices can be easily calculated from the wave functions of the qubit at zero magnetic field. The g-matrix formalism therefore provides the complete dependence of the Larmor and Rabi frequencies on the orientation of the magnetic field at very low computational cost. It also provides a compact model for the control of the qubit, and a simple framework for the analysis of the effects of symmetries on the anisotropy of the Larmor and Rabi frequencies.The g-matrix formalism applies to a wide variety of electron and hole qubits, and we focus on a hole qubit in a silicon-on-insulator nanowire as an illustration. We show that the Rabi frequency of this qubit shows a complex dependence on the orientation of the magnetic field, and on the gate voltages that control the symmetry of the hole wave functions. We point out that the qubit may be advantageously switched between two bias points, one where it can be manipulated efficiently, and one where it is largely decoupled from the gate field but presumably longer lived. We also discuss the role of residual strains in such devices in relation to recent experiments. arXiv:1807.09185v2 [quant-ph]

We analyze a prototypical particle-in-a-box model for a hole spin qubit. This quantum dot is subjected to static magnetic and electric fields, and to a radio-frequency electric field that drives Rabi oscillations owing to spin-orbit coupling. We derive the equations for the Rabi frequency in a regime where the Rabi oscillations mostly result from the coupling between the qubit states and a single nearby excited state. This regime has been shown to prevail in, e.g., hole spin qubits in thin silicon-on-insulator nanowires. The equations for the Rabi frequency highlight the parameters that control the Rabi oscillations. We show, in particular, that [110]-oriented dots on (001) substrates perform much better than [001]-oriented dots because they take best advantage of the anisotropy of the valence band of the host material. We also conclude that silicon provides the best opportunities for fast Rabi oscillations in this regime despite small spin-orbit coupling.