En Garde! Unguarded Iteration for Reversible Computation in the Delay Monad

Kaarsgaard, Robin; Veltri, Niccolò

doi:10.1007/978-3-030-33636-3_13

Cited by 6 publications

(6 citation statements)

References 33 publications

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“…Π is a reversible combinator language introduced in [Bowman et al 2011;James and Sabry 2012] to study strongly typed reversible classical programming. Many extensions exist, such as partiality and iteration [Bowman et al 2011;James and Sabry 2012], fractional types [Chen et al 2020;Chen and Sabry 2021], negative types [Chen and Sabry 2021], and higher combinators [Carette and Sabry 2016;Kaarsgaard and Veltri 2019]. This section introduces a quantum extension to Π, and shows it to be approximately universal for unitaries, the canonical model of pure quantum computation (without measurement).…”

Section: Three Generations Of Yuppiementioning

confidence: 99%

Quantum information effects

Heunen

Kaarsgaard

2022

Proc. ACM Program. Lang.

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We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including measurement. We provide universal categorical constructions that semantically interpret this arrow metalanguage with choice, starting with any rig groupoid interpreting the reversible base language. Several properties of quantum measurement follow in general, and we translate (noniterative) quantum flow charts into our language. The semantic constructions turn the category of unitaries between Hilbert spaces into the category of completely positive trace-preserving maps, and they turn the category of bijections between finite sets into the category of functions with chosen garbage. Thus they capture the fundamental theorems of classical and quantum reversible computing of Toffoli and Stinespring.

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Section: Three Generations Of Yuppiementioning

confidence: 99%

Quantum information effects

Heunen

Kaarsgaard

2022

Proc. ACM Program. Lang.

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“…Π is a reversible combinator language introduced in [4,19] to study strongly typed reversible classical programming. Many extensions exist, such as partiality and iteration [4,19], fractional types [6,7], negative types [7], and higher combinators [5,22]. This section introduces a quantum extension to Π, and shows it to be approximately universal for unitaries, the canonical model of pure quantum computation (without measurement).…”

Section: Three Generations Of Yuppiementioning

confidence: 99%

Quantum Information Effects

Heunen,

Kaarsgaard

2021

Preprint

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We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including measurement. We provide universal categorical constructions that semantically interpret this arrow metalanguage with choice, starting with any rig groupoid interpreting the reversible base language. Several properties of quantum measurement follow in general, and we translate quantum flow charts into our language. The semantic constructions turn the category of unitaries between Hilbert spaces into the category of completely positive trace-preserving maps, and they turn the category of bijections between finite sets into the category of functions with chosen garbage. Thus they capture the fundamental theorems of classical and quantum reversible computing of Toffoli and Stinespring.

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“…In the finitary setting, type isomorphisms provide a perfect, sound and complete, foundation for reversible programming languages [Fiore 2004;Fiore et al 2006;James and Sabry 2012a]. This simple model can be extended by relaxing the isomorphisms to be partial -giving models for Turing-complete reversible languages [Bowman et al 2011; James and Sabry 2012a; Kaarsgaard and Veltri 2019] and by incorporating reversible effects such as state [Heunen et al 2018;Heunen and Karvonen 2015]. The simple model of type isomorphisms was also recently extended by Chen et al [2020] with the same fractional types we use in this paper.…”

Section: Introductionmentioning

confidence: 99%

A computational interpretation of compact closed categories: reversible programming with negative and fractional types

Chen

Sabry

2021

Proc. ACM Program. Lang.

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Compact closed categories include objects representing higher-order functions and are well-established as models of linear logic, concurrency, and quantum computing. We show that it is possible to construct such compact closed categories for conventional sum and product types by defining a dual to sum types, a negative type, and a dual to product types, a fractional type. Inspired by the categorical semantics, we define a sound operational semantics for negative and fractional types in which a negative type represents a computational effect that ``reverses execution flow'' and a fractional type represents a computational effect that ``garbage collects'' particular values or throws exceptions. Specifically, we extend a first-order reversible language of type isomorphisms with negative and fractional types, specify an operational semantics for each extension, and prove that each extension forms a compact closed category. We furthermore show that both operational semantics can be merged using the standard combination of backtracking and exceptions resulting in a smooth interoperability of negative and fractional types. We illustrate the expressiveness of this combination by writing a reversible SAT solver that uses backtracking search along freshly allocated and de-allocated locations. The operational semantics, most of its meta-theoretic properties, and all examples are formalized in a supplementary Agda package.

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En Garde! Unguarded Iteration for Reversible Computation in the Delay Monad

Cited by 6 publications

References 33 publications

Quantum information effects

Quantum information effects

Quantum Information Effects

A computational interpretation of compact closed categories: reversible programming with negative and fractional types

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