  The ground state configurations of the solution to Skyrme's topological
soliton model for systems with baryon number larger than 1 are well
approximated with rational map ans\"atze, without individual baryon
coordinates. Here canonical quantization of the baryon number 2 system, which
represents the deuteron, is carried out in the rational map approximation. The
solution, which is described by the 6 parameters of the chiral group
SU(2)$\times$SU(2), is stabilized by the quantum corrections. The matter
density of the variational quantized solution has the required exponential
large distance falloff and the quantum numbers of the deuteron. Similarly to
the axially symmetric semiclassical solution, the radius and the quadrupole
moment are, however, only about half as large as the corresponding empirical
values. The quantized deuteron solution is constructed for representations of
arbitrary dimension of the chiral group.
