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Granthi: Higher-Order Quantum Programming via Unitary Wiring

Year: 2026

Type: article

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—the paper’s running example, compiled to a static circuit—as well as interference on control-flow history and structured finite control, all within the purely unitary fragment.

Source: Proceedings of the ACM on Programming Languages

DOI: 10.1145/3839496

Authors: Samson Abramsky, Radha Jagadeesan

Institutions: University College London, DePaul University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7204091305

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