  Reservoir computing aims to achieve high-performance and low-cost machine
learning with a dynamical system as a reservoir. However, in general, there are
almost no theoretical guidelines for its high-performance or optimality. This
paper focuses on the reservoir computing with the Kuramoto model and
theoretically reveals its approximation ability. The main result provides an
explicit expression of the dynamics of the Kuramoto reservoir by using the
order parameters. Thus, the output of the reservoir computing is expressed as a
linear combination of the order parameters. As a corollary, sufficient
conditions on hyperparameters are obtained so that the set of the order
parameters gives the complete basis of the Lebesgue space. This implies that
the Kuramoto reservoir has a universal approximation property. Furthermore, the
conjecture on {\it the edge of bifurcation}, which is a generalization of the
famous criterion {\it the edge of chaos} for designing a high-performance
reservoir, is also discussed from the viewpoint of its approximation ability.
It is numerically demonstrated by a prediction task and a transformation task.
