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We present the recent works [1] 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.

Perturbation theory based on Darboux transformation on one-dimensional Dirac equation in Quantum Computation