  The Deutsch model of quantum computation is extended to allow for
thermodynamically irreversible operations by allowing the system of interest to
interact with an outside reservoir. A set of irreversible logical error
correction superoperators are constructed which allow the rapid concentration
of probability from an exponentially large search space into a small number of
logically defined states. These capabilities are used to construct a linear
time solution algorithm for the NP complete problem 3SAT.
