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We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…

Quantum Physics · Physics 2008-05-06 Thorsten Altenkirch , Jonathan Grattage

This paper gives an introduction to and overview of the functional quantum programming language QML. The syntax of this language is defined and explained, along with a new QML definition of the quantum teleport algorithm. The categorical…

Quantum Physics · Physics 2008-07-21 Jonathan Grattage

We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…

Quantum Physics · Physics 2025-11-27 Jun Inoue

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 Physics · Physics 2007-05-23 Wolfgang Mauerer

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…

Logic in Computer Science · Computer Science 2024-03-06 Alejandro Díaz-Caro , Emmanuel Hainry , Romain Péchoux , Mário Silva

Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its…

Programming Languages · Computer Science 2023-11-16 Kartik Singhal , Kesha Hietala , Sarah Marshall , Robert Rand

We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…

Logic in Computer Science · Computer Science 2019-10-02 Mingsheng Ying , Li Zhou , Yangjia Li

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…

Programming Languages · Computer Science 2025-08-08 Finn Voichick , Liyi Li , Robert Rand , Michael Hicks

We present an imperative quantum programming language LanQ which was designed to support combination of quantum and classical programming and basic process operations - process creation and interprocess communication. The language can thus…

Quantum Physics · Physics 2016-09-08 Hynek Mlnarik

We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of…

Quantum Physics · Physics 2013-07-19 Jarosław Adam Miszczak

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…

Logic in Computer Science · Computer Science 2020-08-13 Stefano Guerrini , Simone Martini , Andrea Masini

Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…

Quantum Physics · Physics 2007-05-23 Philippe Jorrand , Marie Lalire

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…

Quantum Physics · Physics 2007-05-23 Philip Maymin

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…

Quantum Physics · Physics 2026-02-25 Vinit Singh , Amandeep Singh Bhatia , Mandeep Kaur Saggi , Manas Sajjan , Sabre Kais

We set down the principles behind a modeling language for quantum software. We present a minimal set of extensions to the well-known Unified Modeling Language (UML) that allows it to effectively model quantum software. These extensions are…

Quantum Physics · Physics 2020-07-01 Carlos A. Perez-Delgado , Hector G. Perez-Gonzalez

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…

Quantum Physics · Physics 2026-02-20 Jacques Carette , Chris Heunen , Robin Kaarsgaard , Neil J. Ross , Amr Sabry

We introduce an abstract machine architecture for classical/quantum computations---including compilation---along with a quantum instruction language called Quil for explicitly writing these computations. With this formalism, we discuss…

Quantum Physics · Physics 2017-02-20 Robert S. Smith , Michael J. Curtis , William J. Zeng

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…

Logic in Computer Science · Computer Science 2014-12-31 Kenta Cho

In this work we introduce Qumin, a novel quantum programming language with a focus on providing an easy to use, minimalist, high-level, and easily extensible platform for quantum programming. Qumin's design concentrates on encompassing the…

Programming Languages · Computer Science 2017-04-17 Alexander Singh , Konstantinos Giannakis , Theodore Andronikos

Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks (e.g., classification/regression). The search for ideal QML models is an active research field. This includes…

Quantum Physics · Physics 2022-02-07 Mahabubul Alam , Swaroop Ghosh
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