Related papers: Regular language quantum states
We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known…
Recent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a…
Quantum computing is a growing field where the information is processed by two-levels quantum states known as qubits. Current physical realizations of qubits require a careful calibration, composed by different experiments, due to noise and…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
Quantum hypergraph states emerged in the literature as a generalization of graph states, and since then, considerable progress has been made toward implementing this class of genuine multipartite entangled states for quantum information and…
Verification and characterisation of quantum states are crucial for the implementation of quantum information processing, especially for many-body systems such as cluster states in optical lattices. In theory, it is simple to estimate the…
Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…
A suitable state representation is a fundamental part of the learning process in Reinforcement Learning. In various tasks, the state can either be described by natural language or be natural language itself. This survey outlines the…
An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
"Natural Language," whether spoken and attended to by humans, or processed and generated by computers, requires networked structures that reflect creative processes in semantic, syntactic, phonetic, linguistic, social, emotional, and…
In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum…
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…