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Pattern Recognition In Non-Kolmogorovian Structures
We present a generalization of the problem of pattern recognition to
arbitrary probabilistic models. This version deals with the problem of
recognizing an individual pattern among a family of different species or
classes of objects which obey probabilistic laws which do not comply with
Kolmogorov's axioms. We show that such a scenario accommodates many important
examples, and in particular, we provide a rigorous definition of the classical
and the quantum pattern recognition problems, respectively. Our framework
allows for the introduction of non-trivial correlations (as entanglement or
discord) between the different species involved, opening the door to a new way
of harnessing these physical resources for solving pattern recognition
problems. Finally, we present some examples and discuss the computational
complexity of the quantum pattern recognition problem, showing that the most
important quantum computation algorithms can be described as non-Kolmogorovian
pattern recognition problems
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
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