  We investigate a general class of dissipative quantum circuit capable of
computing arbitrary Conjunctive Normal Form (CNF) Boolean formulas. In
particular, the clauses in a CNF formula define a local generator of Markovian
quantum dynamics which acts on a network of qubits. Fixed points of this
dynamical system encode the evaluation of the CNF formula. The structure of the
corresponding quantum map partitions the Hilbert space into sectors, according
to decoherence-free subspaces (DFSs) associated with the dissipative dynamics.
These sectors then provide a natural and consistent way to classify quantum
data (i.e. quantum states). Indeed, the attractive fixed points of the network
allow one to learn the sector(s) for which some particular quantum state is
associated. We show how this structure can be used to dissipatively prepare
quantum states (e.g. entangled states), and outline how it may be used to
generalize certain classical computational learning tasks.
