Resource-Aware Hybrid Quantum Programming with General Recursion and Quantum Control

2025-10-23

AI Summary

Existing quantum program resource analysis relies on predefined gate sets and struggles to support general recursion and quantum control. To address this, we propose HyrQL, a hybrid quantum programming language designed for resource analysis. HyrQL imposes no a priori constraints on the initial quantum gate set and natively supports general recursion and quantum control. Via a semantics-preserving compilation algorithm, HyrQL programs are translated into a simply-typed term rewriting system, enabling generic, compositional analysis of time and space complexity for quantum programs. This is the first work achieving gate-set-agnostic resource analyzability in a hybrid quantum language supporting both recursion and quantum control. Experimental evaluation demonstrates the effectiveness and reusability of our approach across diverse gate sets—including standard, Clifford+T, and rotation-based sets—for canonical quantum algorithms such as Grover’s search and the quantum Fourier transform.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

This paper introduces the hybrid quantum language with general recursion $mathtt{Hyrql}$, driven towards resource-analysis. By design, $mathtt{Hyrql}$ does not require the specification of an initial set of quantum gates and, hence, is well amenable towards a generic cost analysis. Indeed, languages using different sets of quantum gates lead to representations of quantum circuits whose complexity varies. Towards resource-analysis, a semantics-preserving compilation algorithm to simply-typed term rewrite systems is described; allowing a generic reuse of all known techniques for analyzing the complexity of term rewrite systems. We prove the versatility of this approach through many examples.

Problem

• Developing quantum language with general recursion for resource analysis
• Enabling generic cost analysis without predefined quantum gates
• Compiling quantum programs to term rewrite systems for complexity analysis

Innovation

• Hybrid quantum language with general recursion
• Semantics-preserving compilation to term rewrite systems
• Generic cost analysis without initial gate specification