Parameterized Verification of Quantum Circuits (Technical Report)

2025-11-24

AI Summary

This work addresses the challenge of verifying input-output correctness and functional equivalence for parameterized quantum circuits. We propose a fully automated relational verification framework based on Synchronized Weighted Tree Automata (SWTA). Our approach constructs compact symbolic models that precisely characterize infinite families of parameterized quantum states, and introduces a quantum gate semantic translator along with a parameterized circuit composition algorithm. This enables, for the first time, formal decision procedures for functional inclusion and equivalence of scalable quantum programs—without reliance on concrete parameter instantiations. The framework supports rigorous, proof-carrying relational verification. Experimental evaluation on canonical parameterized quantum programs—including QAOA and VQE circuits—demonstrates verification times ranging from milliseconds to seconds, confirming both strong expressive power and high practicality.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We present the first fully automatic framework for verifying relational properties of parameterized quantum programs, i.e., a program that, given an input size, generates a corresponding quantum circuit. We focus on verifying input-output correctness as well as equivalence. At the core of our approach is a new automata model, synchronized weighted tree automata (SWTAs), which compactly and precisely captures the infinite families of quantum states produced by parameterized programs. We introduce a class of transducers to model quantum gate semantics and develop composition algorithms for constructing transducers of parameterized circuits. Verification is reduced to functional inclusion or equivalence checking between SWTAs, for which we provide decision procedures. Our implementation demonstrates both the expressiveness and practical efficiency of the framework by verifying a diverse set of representative parameterized quantum programs with verification times ranging from milliseconds to seconds.

Problem

• Verifying relational properties of parameterized quantum programs automatically
• Developing automata models to capture infinite quantum state families
• Checking functional equivalence between parameterized quantum circuits

Innovation

• Automated verification framework for parameterized quantum programs
• Synchronized weighted tree automata model quantum states
• Transducer-based composition algorithms verify circuit equivalence