  Quantum ensemble classification has significant applications in
discrimination of atoms (or molecules), separation of isotopic molecules and
quantum information extraction. However, quantum mechanics forbids
deterministic discrimination among nonorthogonal states. The classification of
inhomogeneous quantum ensembles is very challenging since there exist
variations in the parameters characterizing the members within different
classes. In this paper, we recast quantum ensemble classification as a
supervised quantum learning problem. A systematic classification methodology is
presented by using a sampling-based learning control (SLC) approach for quantum
discrimination. The classification task is accomplished via simultaneously
steering members belonging to different classes to their corresponding target
states (e.g., mutually orthogonal states). Firstly a new discrimination method
is proposed for two similar quantum systems. Then an SLC method is presented
for quantum ensemble classification. Numerical results demonstrate the
effectiveness of the proposed approach for the binary classification of
two-level quantum ensembles and the multiclass classification of multilevel
quantum ensembles.
