Structuring quantum effects: superoperators as arrows

Vizzotto, Juliana Kaizer; Altenkirch, Thorsten; Sabry, Amr

doi:10.1017/s0960129506005287

Cited by 31 publications

(26 citation statements)

References 17 publications

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“…Similarly to lists, sets constitute a monad, but cannot be made an instance of the standard monad class because this class does not allow constraints on the result type. Finite vectors [47] are another example of constrained monads, and there is a recurring need for constrained monads in the context of domain specific languages [8,36].…”

Section: Monadic Notionsmentioning

confidence: 99%

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Supermonads: one notion to bind them all

Bracker

Nilsson

2016

Proceedings of the 9th International Symposium on Haskell

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Several popular generalizations of monads have been implemented in Haskell. Unfortunately, because the shape of the associated type constructors do not match the standard Haskell monad interface, each such implementation provides its own type class and versions of associated library functions. Furthermore, simultaneous use of different monadic notions can be cumbersome as it in general is necessary to be explicit about which notion is used where. In this paper we introduce supermonads: an encoding of monadic notions that captures several different generalizations along with a version of the standard library of monadic functions that work uniformly with all of them. As standard Haskell type inference does not work for supermonads due to their generality, our supermonad implementation is accompanied with a language extension, in the form of a plugin for the Glasgow Haskell Compiler (GHC), that allows type inference for supermonads, obviating the need for manual annotations.

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Section: Monadic Notionsmentioning

confidence: 99%

“…However, this is not the case. The vectors [40,47] briefly mentioned in Section 2 require an equality constraint on the Return instance and they also require a constraint on a in the Bind instance. Another example where constraints in any of these locations are necessary would be embedded domain specific languages [8,36].…”

Section: Representation In Haskellmentioning

confidence: 99%

Supermonads: one notion to bind them all

Bracker

Nilsson

2016

Proceedings of the 9th International Symposium on Haskell

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“…Following this idea of using a monad for non-determinism, the second author of the present paper modeled, in [5], pure quantum vector states and unitary transformations using a Kleisli triple (T, η, * ) that gives a category of pure quantum programs defined as follows: T A = P(A×C), where P(A×C) is the power set over A×C. The function η A is the singleton map a → {(a, 1)}, and if f : A → T B and q ∈ T A, then f…”

Section: Quantum Monadmentioning

confidence: 99%

“…Below we summarize the work presented in [5], as a quantum monad implementation using the Haskell functional programming language. The Java quantum library discussed in next section is based in this presentation.…”

Section: Quantum Monadmentioning

confidence: 99%

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QJava: A Monadic Java Library for Quantum Programming

Vizzotto

Calegaro

2015

RITA

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Abstract:To help the understanding and development of quantum algorithms there is an effort focused on the investigation of new semantic models and programming languages for quantum computing. Researchers in computer science have the challenge of developing programming languages to support the creation, analysis, modeling and simulation of high level quantum algorithms. Based on previous works that use monads inside the programming language Haskell to elegantly explain the odd characteristics of quantum computation (like superposition and entanglement), in this work we present a monadic Java library for quantum programming. We use the extension of the programming language Java called BGGA Closure, that allow the manipulation of anonymous functions (closures) inside Java. We exemplify the use of the library with an implementation of the Toffoli quantum circuit.

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Superoperators for Quantum Software Engineering

Mauerer

2024

Quantum Software

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As implementations of quantum computers grow in size and maturity, the question of how to program this new class of machines is attracting increasing attention in the software engineering domain. Yet, many questions from how to design expressible quantum languages augmented with formal semantics via implementing appropriate optimizing compilers to abstracting details of machine properties in software systems remain challenging. Performing research at this intersection of quantum computing and software engineering requires sufficient knowledge of the physical processes underlying quantum computations, and how to model these. In this chapter, we review a superoperator-based approach to quantum dynamics, as it can provide means that are sufficiently abstract, yet concrete enough to be useful in quantum software and systems engineering, and outline how it is used in several important applications in the field.

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Structuring quantum effects: superoperators as arrows

Cited by 31 publications

References 17 publications

Supermonads: one notion to bind them all

Supermonads: one notion to bind them all

QJava: A Monadic Java Library for Quantum Programming

Superoperators for Quantum Software Engineering

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