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The effects 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 /k₁T. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.
W. G. Unruh (1995) studied this question.
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