A feasible and unitary quantum programming language

Alejandro Díaz-Caro (1, 2, 3) , Emmanuel Hainry (4) , Romain Péchoux (4) , Mário Silva (4)

1 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
2 UBA - Universidad de Buenos Aires [Buenos Aires]
3 UNQ - Universidad Nacional de Quilmes
4 MOCQUA - Designing the Future of Computational Models

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.

Mots clés: Quantum control; Linear Logic; Dual Light Affine Logic

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

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