The effect of resonance on qudit dynamics

Abstract

When the wave nature of particles plays a role in their scattering dynamics, quasi-bound states in the positive energy continuum can have a huge impact on their dynamics. This effect has been observed in nuclear scattering processes and molecular reaction dynamics. We here examine the effect of quasibound state formation in a quantum gate, and its impact on the dynamics of qudits that pass through the quantum gate. The analysis is performed using reaction matrix (R-matrix) theory, with Dirichlet boundary conditions. R-matrix theory obtains results much more efficiently than more computationally demanding methods such as mode matching techniques, tight binding Green’s function methods, or finite element methods.