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

TL;DR

This paper introduces a mathematical model for a quantum transistor based on Dirac potential tuning, utilizing electromagnetic fields and Darboux transformations to control quantum logic gates through relativistic spin qubits.

Contribution

It presents a novel approach combining Dirac potential tuning, Darboux transformations, and electromagnetic field control to implement quantum logic gates in a relativistic quantum transistor.

Findings

Potential for precise quantum gate control via electromagnetic tuning.

Integration of Dirac equation and Darboux transformations for quantum computing.

Energy and qubit state manipulation through control and cyclic operators.

Abstract

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.