Granthi: Higher-Order Quantum Programming via Unitary Wiring

Abstract:Existing quantum programming languages confine higher order structure to a classical host while restricting the quantum layer to first order operations on qubits. This paper presents Granthi, a purely unitary higher-order quantum programming language built on three design commitments: quantum programs are first class values that may be passed, returned, and coherently composed; additive structure is tag-preserving routing rather than observational branching, so control may remain in superposition; and programmer-facing finite label types with named reversible operations provide domain-level control spaces without exposing tag management. Every well-typed term, including at function type, denotes a unitary on its boundary interface, and the compiler realizes exactly its wiring as a quantum circuit on the physical qubit layout (assuming correctness of the pytket backend). Granthi is implemented end-to-end: an OCaml DSL elaborates surface programs through a binder-free core IR to executable quantum circuits via pytket. The language directly supports the quantum switch, compiled to a static circuit, as well as interference on control-flow history and structured finite control, all within the purely unitary fragment.

OOPSLA 2026. this https URL

Quantum Physics (quant-ph); Emerging Technologies (cs.ET); Logic in Computer Science (cs.LO); Programming Languages (cs.PL)

arXiv:2608.20443 [quant-ph]

(or arXiv:2608.20443v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.20443 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.