Granthi: Higher-Order Quantum Programming via Unitary Wiring
Abstract
Many mainstream 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 staged reversible-operation bindings provide domain-level control spaces without exposing tag management. These bindings are eliminated by elaboration before Source typing. Granthi deterministically normalizes each Source program to a canonical wiring form. Every well-typed Source program, including a term of function type, has a unitary boundary interpretation. Under backend correctness (BC), the reference compiler produces a unitary circuit realizing that interpretation. Granthi's currently supported executable fragment is implemented end-to-end: an OCaml DSL elaborates surface programs through a higher-order Core IR to executable quantum circuits via pytket. The language directly supports the pure-unitary quantum switch for explicitly supplied operations; closed instances compile to static circuits. It also supports interference on control-flow history and structured finite control, all within the purely unitary fragment
Related
- The wiring sets a phase-blind quantum memory's gap, the weight caps its coherence
- Optimising Cryogenic Wiring for Microwave-frequency Millikelvin Quantum Processors
- Observation of Scaling of Higher-Order Flow in a Unitary Fermi Gas
- Enabling chemically accurate quantum phase estimation in the early fault-tolerant regime via unitary weight concentration
- Unitary quantum conformal Bondi-Metzner-Sachs field theories
BibTeX
@misc{abramsky2026granthi,
title = {{Granthi: Higher-Order Quantum Programming via Unitary Wiring}},
author = {Samson Abramsky and Radha Jagadeesan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.20443},
eprint = {2608.20443},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20443},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Granthi: Higher-Order Quantum Programming via Unitary Wiring
AU - Samson Abramsky
AU - Radha Jagadeesan
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.20443
UR - https://arxiv.org/abs/2608.20443
AB - Many mainstream 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 staged reversible-operation bindings provide domain-level control spaces without exposing tag management. These bindings are eliminated by elaboration before Source typing. Granthi deterministically normalizes each Source program to a canonical wiring form. Every well-typed Source program, including a term of function type, has a unitary boundary interpretation. Under backend correctness (BC), the reference compiler produces a unitary circuit realizing that interpretation. Granthi's currently supported executable fragment is implemented end-to-end: an OCaml DSL elaborates surface programs through a higher-order Core IR to executable quantum circuits via pytket. The language directly supports the pure-unitary quantum switch for explicitly supplied operations; closed instances compile to static circuits. It also supports interference on control-flow history and structured finite control, all within the purely unitary fragment
ER -