2023/11/02 by Díaz-Caro, Alejandro, Hainry, Emmanuel, Péchoux, Romain +1
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Programming Languages (cs.PL)
paper · doi:10.48550/arxiv.2311.01054
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and polynomial-time normalization. Unitarity is achieved by using a special modality forsuperpositions while requiring orthogonality among superposed terms. Polynomial-time normalization isachieved using a linear-logic-based type discipline employing Barber and Plotkin duality along with a specificmodality to account for potential duplications. This type discipline also guarantees that derived values havepolynomial size. Our language seamlessly combines the two modalities: quantum circuit programs upholdunitarity, and all programs are evaluated in polynomial time, ensuring their feasibility.