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Preprints, Working Papers, ... Year : 2022

The Many-Worlds Calculus

Abstract

We propose a new typed graphical language for quantum computation, based on compact categories with biproducts. Our language generalizes existing approaches such as ZX-calculus and quantum circuits, while offering a natural framework to support quantum control: it natively supports "quantum tests". The language comes equipped with a denotational semantics based on linear applications, and an equational theory. Through the use of normal forms for the diagrams, we prove the language to be universal, and the equational theory to be complete with respect to the semantics.
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Dates and versions

hal-03654190 , version 1 (28-04-2022)
hal-03654190 , version 2 (03-08-2022)

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Cite

Kostia Chardonnet, Marc de Visme, Benoît Valiron, Renaud Vilmart. The Many-Worlds Calculus. 2022. ⟨hal-03654190v2⟩
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