  The amount of heat generated by computers is rapidly becoming one of the main
problems for developing new generations of information technology. The
thermodynamics of computation sets the ultimate physical bounds on heat
generation. A lower bound is set by the Landauer Limit, at which computation
becomes thermodynamically reversible. For classical computation there is no
physical principle which prevents this limit being reached, and approaches to
it are already being experimentally tested. In this paper we show that for
quantum computation there is an unavoidable excess heat generation that renders
it inherently thermodynamically irreversible. The Landauer Limit cannot, in
general, be reached by quantum computers. We show the existence of a lower
bound to the heat generated by quantum computing that exceeds that given by the
Landauer Limit, give the special conditions where this excess cost may be
avoided, and show how classical computing falls within these special
conditions.
