HUGR: A Quantum-Classical Intermediate Representation

2025-10-13

AI Summary

Hybrid quantum-classical programs lack an intermediate representation (IR) that simultaneously ensures expressiveness, scalability, and formal guarantees. Method: This paper introduces HUGR—a hierarchical, graph-based IR integrating a static type system with a linear quantum type system to enforce quantum resource safety; inspired by MLIR, it supports multi-level abstraction refinement and pattern-matching compilation, enabling unified modeling of near-term NISQ devices, future fault-tolerant architectures, and emerging quantum programming paradigms. Contribution/Results: HUGR balances machine efficiency with human readability, facilitating scalable toolchain development and formal verification. We provide a complete formal specification, an open-source reference implementation, and empirically validate its expressiveness, compilation efficiency, and type safety on real-world quantum programs.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We introduce the Hierarchical Unified Graph Representation (HUGR): a novel graph based intermediate representation for mixed quantum-classical programs. HUGR's design features high expressivity and extensibility to capture the capabilities of near-term and forthcoming quantum computing devices, as well as new and evolving abstractions from novel quantum programming paradigms. The graph based structure is machine-friendly and supports powerful pattern matching based compilation techniques. Inspired by MLIR, HUGR's extensibility further allows compilation tooling to reason about programs at multiple levels of abstraction, lowering smoothly between them. Safety guarantees in the structure including strict, static typing and linear quantum types allow rapid development of compilation tooling without fear of program invalidation. A full specification of HUGR and reference implementation are open-source and available online.

Problem

• Develops hierarchical graph representation for quantum-classical programs
• Enables extensible compilation across multiple abstraction levels
• Provides safety guarantees through static typing and linear types

Innovation

• Graph-based intermediate representation for quantum-classical programs
• Extensible design supporting multiple abstraction levels
• Strict static typing with linear quantum type safety