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

TL;DR

This paper explores how Darboux transformations applied to the one-dimensional Dirac equation can advance quantum computation by enabling new physical representations and applications like quantum transistors.

Contribution

It introduces a novel application of Darboux transformation to the Dirac equation in quantum information, linking relativity concepts with quantum-classical trade-offs.

Findings

Darboux transformation enables new physical representations in quantum systems.

Application to cavity QED demonstrates potential for quantum information processing.

Proposal of a quantum transistor based on transformed Dirac equations.

Abstract

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.