Control Protocol for Dynamic Synthesis of Qubit and Qudit Gates Using Photonic Pulses and Magnetic Fields

We propose a theoretical control protocol designed for the dynamic synthesis of single qubit and four-level qudit quantum gates using external parameters, such as photonic Gaussian pulses and magnetic fields, in a microcavity quantum well system. Our approach takes advantage of tunable coherent light matter interactions that can be modulated by the magnetic field between the exciton and negative trion coupled to the lowest photonic mode. We demonstrate that it is possible to achieve precise manipulation of populations of encoded quantum states through the unitary evolution of the system. In particular, we illustrate our optimization method for generating a single qubit gate with a mean fidelity of 99.99 as well as the realization of an iSWAP gate in the four level qudit case with a fidelity of 99.6.