  We elaborate on the quantization of toric varieties by combining techniques
from toric geometry, isospectral deformations and noncommutative geometry in
braided monoidal categories, and the construction of instantons thereon by
combining methods from noncommutative algebraic geometry and a quantised
twistor theory. We classify the real structures on a toric noncommutative
deformation of the Klein quadric and use this to derive a new noncommutative
four-sphere which is the unique deformation compatible with the noncommutative
twistor correspondence. We extend the computation of equivariant instanton
partition functions to noncommutative gauge theories with both adjoint and
fundamental matter fields, finding agreement with the classical results in all
instances. We construct moduli spaces of noncommutative vortices from the
moduli of invariant instantons, and derive corresponding equivariant partition
functions which also agree with those of the classical limit.
