Analytic view on N body interaction in electrostatic quantum gates and decoherence effects in tight-binding model

Abstract

Analytical solutions describing quantum swap and Hadamard gate are given with the use of tight-binding approximation. Decoherence effects are described analytically for 2 interacting electrons confined by local potentials with use of tight-binding simplistic model and in Schroedinger formalism with omission of spin degree of freedom. The obtained results can be generalized for the case of [Formula: see text] electrostatically interacting quantum bodies confined by local potentials ([Formula: see text]-qubit) system representing any electrostatic quantum gate with [Formula: see text] inputs/outputs. The mathematical structure of system evolution with time is specified.