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.