We study systems conformed by two miscible coherently coupled spin components of a spinor Bose gas. When this kind of mixtures are loaded on an atomtronic circuit, like a toroidal potential, they are able to hold persistent currents, i.e. states with topological structure. The duality between the presence and the absence of these currents conform a qubit (in analogy with the Mooij-Harmans qubit in superconductors) and it naturally appears under the implementation of Rabi oscillations in a two-level system. Such qubit can be manipulated by phase slip mechanism, which is allowed by the coherent coupling between both components. We identify the topological consequences of the possibilities offered by the qubit by means of solitonic states that can emerge in the atomtronic circuit. All these properties lead to new perspectives in the building of quantum computer gates as well as the nucleation and analysis of solitary waves and persistent currents.