Electrostatically Interacting Wannier Qubits in Curved Space

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov-Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger's equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices.