  With the help of the Berry curvature and the first Chern number
$($$\textit{C}_1$$)$, we both analytically and numerically investigate and thus
simulate artificial magnetic monopoles formed in parameter space of the
Hamiltonian of a driven superconducting qubit. The topological structure of a
spin-1/2 system $($qubit$)$ can be captured by the distribution of Berry
curvature, which describes the geometry of eigenstates of the Hamiltonian.
Degeneracy points in parameter space act as sources $($$\textit{C}_1$ = $1$$)$
or sinks $($$\textit{C}_1$ = $-1$$)$ of the magnetic field. We note that the
strength of the magnetic field $($described by Berry curvature$)$ has an
apparent impact on the quantum states during the process of topological
transition. It exhibits an unusual property that the transition of the quantum
states is asymmetric when the degenerate point passes from outside to inside
and again outside the manifold spanned by system parameters. Our results also
pave the way to explore intriguing properties of magnetic monopoles in other
spin-1/2 systems.
