Related papers: Regular language quantum states
This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…
An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and…
Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
A unified theory of language combines a Bayesian cognitive linguistic model of language processing, with the proposal that language evolved by sexual selection for the display of intelligence. The theory accounts for the major facts of…
The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical…
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…
Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement,…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate various comet-like types of languages and compare such language…
We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…
A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically…
We present the quantum programming language cQPL which is an extended version of QPL [P. Selinger, Math. Struct. in Comp. Sci. 14(4):527-586, 2004]. It is capable of quantum communication and it can be used to formulate all possible quantum…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and…
Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we…
This report is mostly written for educational purposes. It is meant as a self contained introduction to regular languages, regular expressions, and regular expression matching by using Brzozowski derivatives. As such it is mostly based on…
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…