Robust Sub-Kelvin Simulations of Quantum Dot Charge Sensing

Spin-qubit-based quantum computing technologies commonly involve quantum point contacts (QPCs). Indeed, the conductance quantization exhibited by QPCs may be harnessed for the sensing of the charge in a quantum dot (QD) which may, in turn, be harnessed for spin-qubit characterization and readout. In this work, we report a self-consistent finite-element method (FEM) simulation scheme for QD charge sensing by a QPC in planar semiconductor heterostructures. This scheme fully accounts for the electrostatics, quantum confinement, and quantum transport phenomena that are relevant in semiconductor quantum wells (QWs). Robust sub-Kelvin convergence is achieved partly thanks to an adaptive meshing algorithm for Poisson’s equation and partly thanks to the uncertainty principle, which leads to diffuse charge density profiles. To minimize computational burden, we leverage the quasi-separability of the Schrödinger equation in the QW, turning a 3D problem into a set of 1D problems; furthermore, we leverage the sub-Kelvin temperature to reduce the calculation of the QPC’s conductance to a single Green’s function evaluation. Finally, we report: (A) simulations of the hole density in an AlGaAs–GaAs QW accurately matching experimental data and (B) charge sensing in simulations of realistic QD and QPC devices, thereby demonstrating our simulation scheme’s relevance to the modeling of spin qubit technologies.