  The key difficulty in the modelling of large quantum coherent structures lies
in keeping track of nonlocal, multipoint quantum correlations between their
constituent parts. Here we consider a special case of such a system, a fractal
quantum metamaterial interacting with electromagnetic field, and show that it
can be exactly solved by using a combination of the Haar transform and the
Wigner-Weyl transform. Theoretical and experimental investigation of
finite-size precursors to exactly solvable fractal quantum structures as this
will help illuminate the behaviour of generic quantum coherent structures on a
similar spatio-temporal scale.
