In this letter we present a scheme for generating maximally entangled states of two cavity modes which enables us to generate complete set of Bell basis states having rather simple initial state preparation. Furthermore, we study the interaction of a two-level atom with two modes of electromagnetic field in a high Q cavity. The two-level atom acts as a control qubit and the two mode electromagnetic field serves as a target qubit. This simple system of quantum electrodynamics provides us experimentally feasible universal quantum logic gates.
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
{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.
Quantum logic operations are the elemental operations for quantum computing and have been implemented in various time-evolved atomic systems. Here, we present a scheme to simulatively implement the typical quantum NOT- and Hadamard gates operations, alternatively with the coupled three-waveguide structure (rather than the usual atomic levels); two modes in sinuous waveguides encoding the two logic states of a qubit and the mode in the center straight waveguide serve as auxiliary the coupler. Based on the Lewis-Riesenfeld invariant theory, we show that the desired mode conversions for implementing the NOT gate and mode split to realize the Hadamard gate are fast achieved by engineering the coupling parameters between the optical waveguides. The implementations of the logic gates demonstrated here relay on the structure parameters of the waveguides, rather than the durations of time evolutions with the usual driven atomic systems, and thus should be feasible robustly with the current integrated optical technology.