  The effect of the inevitable coupling to external degrees of freedom of a
quantum computer are examined. It is found that for quantum calculations (in
which the maintenance of coherence over a large number of states is important),
not only must the coupling be small but the time taken in the quantum
calculation must be less than the thermal time scale, $\hbar/k_B T$. For longer
times the condition on the strength of the coupling to the external world
becomes much more stringent.
