Related papers: Regular language quantum states
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise…
We show the Standard Model and SuperString Theories can be naturally based on a Quantum Computer foundation. The Standard Model of elementary particles can be viewed as defining a Quantum Computer Grammar and language. A Quantum Computer in…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially…
To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free…
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…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is…
The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of $\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its input. T.…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
State preparation compilers for quantum computers typically sit at two extremes: general-purpose routines that treat the target as an opaque amplitude vector, and bespoke constructions for a handful of well-known state families. We ask…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…