Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force

We propose a mathematical model of \textit{quantum} transistor in which bandgap engineering corresponds to the tuning of Dirac potential in the complex four-vector form. The transistor consists of $n$-relativistic spin qubits moving in \textit{classical} external electromagnetic fields. It is shown that the tuning of the direction of the external electromagnetic fields generates perturbation on the potential temporally and spatially, determining the type of quantum logic gates. The theory underlying of this scheme is on the proposal of the intertwining operator for Darboux transfomations on one-dimensional Dirac equation amalgamating the \textit{vector-quantum gates duality} of Pauli matrices. Simultaneous transformation of qubit and energy can be accomplished by setting the $\{\textit{control, cyclic}\}$-operators attached on the coupling between one-qubit quantum gate: the chose of \textit{cyclic}-operator swaps the qubit and energy simultaneously, while \textit{control}-operator ensures the energy conservation.Comment: 23 pages, 10 figures: Typo corrections. A new Subsection with massless Dirac-fermions in a uniform magnetic field is include

Perturbation Theory Based on Darboux Transformation on One-Dimensional Dirac Equation in Quantum Computation

We present the recent works \cite{trisetyarso2011} on the application of Darboux transformation on one-dimensional Dirac equation related to the field of Quantum Information and Computation (QIC). The representation of physical system in one-dimensional equation and its transformation due to the Bagrov, Baldiotti, Gitman, and Shamshutdinova (BBGS)-Darboux transformation showing the possibility admitting the concept of relativity and the trade-off of concurrent condition of quantum and classical physics play into the area of QIC. The applications in cavity quantum electrodynamics and on the proposal of quantum transistor are presented.Comment: 2 pages, 3 figures Information and Communication Technology (ICoICT), 201