This paper explores the self phase modulation of elliptical \(q\) -Gaussian laser beams as they propagate through diffraction-managed nonlinear media, with a focus on their potential applications in quantum computing. The study examines how the beam’s elliptical geometry and \(q\) -Gaussian intensity profile influence both its self-focusing dynamics and axial phase evolution. Employing a variational approach, the analysis investigates the role of intensity-dependent refractive index variations, in conjunction with diffraction management, in governing self-focusing and phase modulation. Special attention is given to the impact of the \(q\) parameter on the beam’s intensity distribution and phase stability. Numerical simulations reveal that higher \(q\) values lead to weaker phase shifts and greater beam stability, while lower \(q\) values result in stronger phase modulation and more dynamic behavior. These results highlight the promise of elliptical \(q\) -Gaussian beams in quantum computing, where precise phase control and stability are essential for secure quantum communication and information processing.
