Realization of quantum gates based on three-dimensional harmonic oscillator in a time-varying electromagnetic field
This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O(e) and \(O({e}^2)\) perturbations and then solving the Schrdinger equation to obtain the evolution operator at time T up to \(O({e}^2)\), and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0,T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.
quantum gate schrdinger equation perturbation theory dyson series 3-d quantum harmonic oscillators lagrange multiplier