  In this study, we address challenges in designing quantum information
processors based on electron spin qubits in electrostatically-defined quantum
dots (QDs). Numerical calculations of charge stability diagrams are presented
for a realistic double QD device geometry. These methods generaize to linear QD
arrays, and are based on determining the effective parameters of a Hubbard
model Hamiltonian that is then diagonalized to find the many-electron ground
state energy. These calculations enable the identification of gate voltage
ranges that maintain desired charge states during qubit manipulation, and also
account for electrical cross-talk between QDs. As a result, the methods
presented here promise to be a valuable tool for developing scalable spin qubit
quantum processors.
