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Monads Need Not Be Endofunctors
"... Abstract. We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finitedimensional vector spaces, untyped and typed λcalculus syntax and indexed containers. We show that the Kleisli and EilenbergMoore constr ..."
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Cited by 19 (5 self)
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Abstract. We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finitedimensional vector spaces, untyped and typed λcalculus syntax and indexed containers. We show that the Kleisli and EilenbergMoore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between monads and relative monads. Arrows are also an instance of relative monads. 1
Quipper: A Scalable Quantum Programming Language
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"... The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higherorder q ..."
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The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higherorder quantum programming language. Quipper has been used to program a diverse set of nontrivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.
MONADS NEED NOT BE ENDOFUNCTORS ∗
, 2011
"... Vol. 11(1:3)2015, pp. 1–40 www.lmcsonline.org ..."
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Compilation to Quantum Circuits for a Language with Quantum Data and Control
"... Abstract—In this paper we further investigate nQML, a functional quantum programming language that follows the “quantum data and control ” paradigm. We define a semantics for nQML, which translates programs to quantum circuits in the category FQC of finite quantum computations, following the approac ..."
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Abstract—In this paper we further investigate nQML, a functional quantum programming language that follows the “quantum data and control ” paradigm. We define a semantics for nQML, which translates programs to quantum circuits in the category FQC of finite quantum computations, following the approach of Altenkirch and Grattage’s QML. This semantics, which coincides with the denotational semantics for nQML over density matrices and unitary transformations, serves as a compiler from nQML programs to quantum circuits. We also provide an implementation of this compiler, written in Haskell, as well as an interpreter for quantum circuits. I.
ScaffCC: A Framework for Compilation and Analysis of Quantum Computing Programs
"... Quantum computing is a promising technology for highperformance computation, but requires mature toolflows that can map largescale quantum programs onto targeted hardware. In this paper, we present a scalable compiler for largescale quantum applications, and show the opportunities for reducing c ..."
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Quantum computing is a promising technology for highperformance computation, but requires mature toolflows that can map largescale quantum programs onto targeted hardware. In this paper, we present a scalable compiler for largescale quantum applications, and show the opportunities for reducing compilation and analysis time, as well as output code size. We discuss the similarities and differences between compiling for a quantum computer as opposed to a classical computer, and present a stateoftheart approach for compilation of classical circuits into quantum circuits. Our work also highlights the importance of highlevel quantum compilation for logical circuit translation, quantitative analysis of algorithms, and optimization of circuit lengths.