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Preprints, Working Papers, ... Year : 2024

A feasible and unitary quantum programming language

Abstract

We introduce a novel quantum programming language featuring higher-order programs and quantum control flow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeing both unitarity and polynomial-time normalization. Unitarity is achieved by using a special modality for superpositions while requiring orthogonality among superposed terms. Polynomial-time normalization is achieved using a linear-logic-based type discipline employing Barber and Plotkin duality along with a specific modality to account for potential duplications. This type discipline also guarantees that derived values have polynomial size. Our language seamlessly combines the two modalities: quantum circuit programs uphold unitarity, and all programs are evaluated in polynomial time, ensuring their feasibility.
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Dates and versions

hal-04266203 , version 1 (31-10-2023)
hal-04266203 , version 2 (15-11-2023)
hal-04266203 , version 3 (04-03-2024)

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Alejandro Díaz-Caro, Emmanuel Hainry, Romain Péchoux, Mário Silva. A feasible and unitary quantum programming language. 2024. ⟨hal-04266203v3⟩
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