Quantum data classification by dissipation.

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 for quantum machine learning. Under this protocol, it is demonstrated, that one can learn non-trivial information about a quantum state in a passive manner, without directly measuring or disturbing the state.