Tunability of qubit Coulomb interaction: Numerical analysis of top gate depletion in two-dimensional electron systems

Abstract

We investigate the tunability of electrostatic coupling between solid state quantum dots as building blocks for quantum bits. Specifically, our analysis is based upon two-dimensional electron systems (2DEG) and depletion by top gates. We are interested in whether the Coulomb interaction between qubits can be tuned by electrical means using screening effects. The systems under investigation are analyzed numerically solving the Poisson equation in 3D via relaxation techniques with optimized algorithms for an extended set of boundary conditions. These include an open outer boundary, simulation of 2DEG systems and dielectric boundaries like the surface of a physical sample. The results show that for currently lithographically available feature sizes, the Coulomb interaction between the quantum bits is weak in general due to efficient screening in the planar geometry of 2DEG and top gates. The evaluated values are on the order of 1 $μ$eV. Moreover, while it is not possible to turn off the qubit interaction completely, an effective tunability on the order of 50% is clearly realizable while maintaining an intact quantum bit structure.