Recognizing Concepts and Recognizing Musical Themes. A Quantum Semantic Analysis

How are abstract concepts and musical themes recognized on the basis of some previous experience? It is interesting to compare the different behaviors of human and of artificial intelligences with respect to this problem. Generally, a human mind that abstracts a concept (say, table) from a given set of known examples creates a table-Gestalt: a kind of vague and out of focus image that does not fully correspond to a particular table with well determined features. A similar situation arises in the case of musical themes. Can the construction of a gestaltic pattern, which is so natural for human minds, be taught to an intelligent machine? This problem can be successfully discussed in the framework of a quantum approach to pattern recognition and to machine learning. The basic idea is replacing classical data sets with quantum data sets, where either objects or musical themes can be formally represented as pieces of quantum information, involving the uncertainties and the ambiguities that characterize the quantum world. In this framework, the intuitive concept of Gestalt can be simulated by the mathematical concept of positive centroid of a given quantum data set. Accordingly, the crucial problem "how can we classify a new object or a new musical theme (we have listened to) on the basis of a previous experience?" can be dealt with in terms of some special quantum similarity-relations. Although recognition procedures are different for human and for artificial intelligences, there is a common method of "facing the problems" that seems to work in both cases.

Pattern recognition on the quantum Bloch sphere

We introduce a framework suitable for describing pattern recognition task using the mathematical language of density matrices. In particular, we provide a one-to-one correspondence between patterns and pure density operators. This correspondence enables us to: i) represent the Nearest Mean Classifier (NMC) in terms of quantum objects, ii) introduce a Quantum Classifier (QC). By comparing the QC with the NMC on different 2D datasets, we show the first classifier can provide additional information that are particularly beneficial on a classical computer with respect to the second classifier.