Universal modeling of electrostatic semiconductor quantum gates of any topology interfaced to Josephson junction quantum circuit

Single electron devices implemented in the chain of coupled quantum dots becomes quite promising way of implementation of qubits [1], quantum logical gates and quantum communication systems due to usage of well-developed CMOS technology that guarantees very high integration. On another hand the superconducting circuits achieved limited level of scalabilty and are the less noisy integrated systems at low temperatures, so they account for scalable superconducting qubits. High level of CMOS scalability and low noise level in case of Josephson junction makes necessary to consider the hybrid superconducting-semiconductor quantum devices and interfaces between them as given by [2-3]. The concept of programmable quantum matter and thus quantum circuits can be modeled by usage of quasi one-dimensional models of semiconductor (superconducting) nanowires in Schrodinger (Bogoliubov-de Gennes) or tight-binding formalisms. In such case, open loop nanowires of arbitrary topology can be approximated by quasi one-dimensional description. The presented scheme can be easily generalized to N interacting electrons placed at N different semiconductor nanowires, whose functionality can be regulated with proper external biasing electric and electromagnetic fields. The interaction of Josephson junction with semiconductor quantum dots is described both by capacitive or inductive channels. In such way, quantum information processing can be studied in dependence on different topologies of semiconductor nanowires in various electromagnetic conditions.