  We construct quantum mechanical observables and unitary operators which, if
implemented in physical systems as measurements and dynamical evolutions, would
contradict the Church-Turing thesis which lies at the foundation of computer
science. We conclude that either the Church-Turing thesis needs revision, or
that only restricted classes of observables may be realized, in principle, as
measurements, and that only restricted classes of unitary operators may be
realized, in principle, as dynamics.
