Related papers: Extending the Lambda Calculus to Express Randomize…
The emergence of noisy medium-scale quantum devices has led to proof-of-concept applications for quantum computing in various domains. Examples include Natural Language Processing (NLP) where sentence classification experiments have been…
We introduce Lambda-SX, a typed quantum lambda-calculus that supports multiple measurement bases. By tracking duplicability relative to arbitrary bases within the type system, Lambda-SX enables more flexible control and compositional…
Large Language Models (LLMs) show strong capabilities in code generation, motivating their use in automated quantum solver development. However, in quantum computing, successful execution of generated code is not sufficient: correctness…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
Natural language processing (NLP) problems are ubiquitous in classical computing, where they often require significant computational resources to infer sentence meanings. With the appearance of quantum computing hardware and simulators, it…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
A few conventions for thinking about and writing quantum pseudocode are proposed. The conventions can be used for presenting any quantum algorithm down to the lowest level and are consistent with a quantum random access machine (QRAM) model…
Question answering (QA) systems are among the most important and rapidly developing research topics in natural language processing (NLP). A reason, therefore, is that a QA system allows humans to interact more naturally with a machine,…
We present a representation for linguistic structure that we call a Fock-space representation, which allows us to embed problems in language processing into small quantum devices. We further develop a formalism for understanding both…
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine…
The main aim of this thesis is to look for a logical deductive calculus (we will adopt sequent calculus, originally introduced in Gentzen, 1935), which could describe quantum information and its properties. More precisely, we intended to…
Probabilistic Programming Languages (PPLs) are a powerful tool in machine learning, allowing highly expressive generative models to be expressed succinctly. They couple complex inference algorithms, implemented by the language, with an…
We study the desiderata on a model for statistical probabilistic programming languages. We argue that they can be met by a combination of traditional tools, namely open bisimulation and probabilistic simulation.
Semantic parsing is a means of taking natural language and putting it in a form that a computer can understand. There has been a multitude of approaches that take natural language utterances and form them into lambda calculus expressions --…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
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…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…