Simulation Framework for Hole Spin Qubits

A framework for the simulation of hole spin qubits based on COMSOL Multiphysics is presented. The tool solves the coupled Poisson and Schrӧdinger equations in the four-bands k⋅p Hamiltonian including the effects of a static magnetic field B. The gyromagnetic matrix g and its derivative g’ with respect to the gate voltage are calculated from the wavefunctions at zero magnetic field. The matrices g and g’ allow for the computation of the Rabi frequency as a function of the magnetic field to first order in the magnetic field and in the gate voltage. Results for a qubit hosted in a silicon nanowire fabricated in SOI technology are presented. Solutions for different gate geometries are compared.