A possibility of quantum evolution of language

D. -F. Qin

This paper examines language modeling based on the theory of quantum mechanics. It focuses on the introduction of quantum mechanics into the symbol-meaning pairs of language in order to build a representation model of natural language. At the same time, it is realized that word embedding, which is widely used as a basic technique for statistical language modeling, can be explained and improved by the mathematical framework of quantum mechanics. On this basis, this paper continues to try to use quantum statistics and other related theories to study the mathematical representation, natural evolution and statistical properties of natural language. It is also assumed that the source of such quantum properties is the physicality of information. The feasibility of using quantum theory to model natural language is pointed out through the construction of a experimental code. The paper discusses, in terms of applications, the possible help of the theory in constructing generative models that are popular nowadays. A preliminary discussion of future applications of the theory to quantum computers is also presented.

V. A. Malyshev

Gustav Herdan

Olivier Brunet, Philippe Jorrand

We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way, the evolution of the system becomes part of the logical study. We show how both unitary operations and two-valued measurements can be included in this formalism and can thus be handled logically.

Charis Anastopoulos

In this paper we are interested in studying coarse graining in field theories using the language of quantum open systems. Motivated by the ideas of Hu and Calzetta on correlation histories we employ the Zwanzig projection technique to obtain evolution equations for relevant observables in self-interacting scalar field theories. Our coarse-graining operation consists in concentrating solely on the evolution of the correlation functions of degree less than $n,$ a treatment which corresponds to the familiar truncation of the BBKGY hierarchy at the $n$th level. We derive the equations governing the evolution of mean-field and two-point functions thus identifying the terms corresponding to dissipation and noise. We discuss possible applications of our formalism, the emergence of classical behavior, and the connection to the decoherent histories framework.

Diederik Aerts, Marek Czachor, Bart D’Hooghe