  Derivation of tight-binding model from Schroedinger formalism for various
topologies of position-based semiconductor qubits is presented in this work in
case of static and time-dependent electric fields. Simplistic tight-binding
model allows for description of single-electron devices at large integration
scale. The case of two electrostatically Wannier qubits (that are also known as
position based qubits) in Schroedinger model is presented with omission spin
degrees of freedom. The concept of programmable quantum matter can be
implemented in the chain of coupled semiconductor quantum dots. Indeed highly
integrated and developed cryogenic CMOS nanostructures can be mapped to coupled
quantum dots, whose connectivity can be controlled by voltage applied across
transistor gates as well as external magnetic field. Using anti-correlation
principle arising from Coulomb repulsion interaction between electrons one can
implement classical and quantum inverter (Classical/Quantum Swap gate) and many
other logical gates. This anti-correlation will be weaken due to the fact of
quantumness of physical process is bringing coexistence of correlation and
anti-correlation at the same time. One of the central results presented in this
work relies on the emergence of dissipation processes during smooth bending of
semiconductor nanowires both in the case of classical and quantum picture. We
observe strong localization of wave-packet due to nanowire bending. The
obtained results can be mapped to problem of electron in curved space, so they
can be expressed by programmable position-dependent metric embedded in
Schroedinger equation. Indeed semiconductor quantum dot system is capable of
mimicking the curved space what provides bridge between fundamental and applied
science present in implementation of single-electron devices.
