  All elementary Hamiltonians in nature are expected to be invariant under
rotation. Despite this restriction, we usually assume that any arbitrary
measurement or unitary time evolution can be implemented on a physical system,
an assumption whose validity is not obvious. We introduce two different schemes
by which any arbitrary unitary time evolution and measurement can be
implemented with desired accuracy by using rotationally invariant Hamiltonians
that act on the given system and two ancillary systems serving as reference
frames. These frames specify the z and x directions and are independent of the
desired time evolution. We also investigate the effects of quantum fluctuations
that inevitably arise due to usage of a finite system as a reference frame and
estimate how fast these fluctuations tend to zero when the size of the
reference frame tends to infinity. Moreover we prove that for a general
symmetry any symmetric quantum operations can be implemented just by using
symmetric interactions and ancillas in the symmetric states.
