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International Journal of Quantum Information

QUANTUM MECHANICS AND PATTERN RECOGNITION

George Chapline

Published Aug 30, 2004• 2 citations
Publisher

Abstract

It has long been known that the Schrodinger equation provides a description of a certain kind of statistical Markov process. We show here that as a consequence, one can view quantum mechanics as an extension of the Helmholtz machine approach to pattern recognition. Not only does this observation throw new light on the relationship between quantum mechanics and computing theory, but it suggests that mathematical techniques developed for inverse scattering problems might provide an alternative to conventional pattern recognition algorithms.

DOI
10.1142/s0219749904000328

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It has long been known that the Schrodinger equation provides a description of a certain kind of statistical Markov process. We show here that as a consequence, one can view quantum mechanics as an extension of the Helmholtz machine approach to pattern recognition. Not only does this observation throw new light on the relationship between quantum mechanics and computing theory, but it suggests that mathematical techniques developed for inverse scattering problems might provide an alternative to conventional pattern recognition algorithms.
We introduce a new approach in dealing with pattern recognition issue. Recognizing a pattern is definitely not the exploration of a new discovery but rather the search for already known patterns. In reading for example the same text written in a hand writing, letters can appear in different shapes. Still, the text decoding corresponds with interpreting the large variety of hand writings shapes with fonts. Quantum mechanics also offer a kind of interpretation tool. Although, with the superposition principle it is possible to compose an infinite number of states, yet, an observer by conducting a measurement reduces the number of observed states into the predetermined basis states. Not only that any state collapses into one of the basis states, quantum mechanics also possesses a kind of correction mechanism in a sense that if the measured state is “close enough” to one of the basis states, it will collapse with high probability into this predetermined state. Thus, we can consider the collapse mechanism as a reliable way for the observer to interpret reality into his frame of concepts. Both interpretation ideas, pattern recognition and quantum measurement are integrated in this paper to formulate a quantum pattern recognition measuring procedure.
Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the “wake‐sleep” algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi‐channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.
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The paper proposes a new approach in the foundations of Quantum Mechanics.It does not make any assumption about the physical world, but looks at the consequences of the formalism used in models.Whenever a system is represented by variables which meet precise, but common, mathematical properties, one can prove theorems which are very close to the axioms of Quantum Mechanics (Hilbert spaces, observables, eigen values,...).It is then possible to explore the conditions of the validity of these axioms and to give a firm ground to the usual computations.Moreover this approach sheds a new ligth on the issues of determism, and interacting systems.In the third edition of this paper developments have been added about the statistical procedures used to detect anomalies in Physical Laws.