Unified modelling theory for qubit representation using quantum field graph models

Abstract

Linear graph theory, a branch of topology, has been applied to such diverse systems as ranging from electrical networks through real physical systems and “conceptual” socio-economic-environmental systems to “esoteric” creational systems. Linear graph theory represents one step towards a systems modelling discipline which coordinates various branches of knowledge into one scientific order. This paper presents a quantum field graph model which is facilitated by considering a qubit as a basic building block and representing it through an appropriate linear graph. The system graph is in two separate parts corresponding to a qubit representation .j iDj0iCj1i/, consisting of “ket 0” and “ket 1” subsystem graphs. Unit “Poynting”-like vectors j0i and j1i behave like quantum across (potential) variables specifying “direction” of information (data)/energy propagation, as it were, while and behave like quantum through (flow-rate or “force”) variables specifying probability parameters for quanta of information (data)/energy flow-rate (energy flux or power flow,
W/m2/. For n independent states, there will be precisely n basis quantum potential vectors (or unit “Poynting” vectors). The model has been successfully applied for several quantum gates as well as applications such as quantum teleportation and has the potential for successfully modelling systems at the high end of complexity scale.