Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach

2025-06-09

AI Summary

Ensuring safety guarantees for quantum circuit verification under uncertainties in initial states and quantum dynamics remains challenging. Method: This paper proposes a barrier certificate synthesis method based on scenario optimization, supporting both finite- and infinite-horizon safety verification. It introduces the scenario approach—previously unexplored in quantum barrier synthesis—to model quantum state evolution, construct Lyapunov-type barrier functions, and solve the synthesis problem via semidefinite programming. Contribution/Results: The method enables provably safe verification of uncertain quantum dynamics. It successfully generates verifiable barrier certificates for multiple benchmark quantum circuits. Experiments demonstrate that polynomial barrier functions achieve an optimal trade-off between verification accuracy and computational efficiency. This work establishes a novel paradigm for reliability verification of quantum hardware and algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In recent years, various techniques have been explored for the verification of quantum circuits, including the use of barrier certificates, mathematical tools capable of demonstrating the correctness of such systems. These certificates ensure that, starting from initial states and applying the system's dynamics, the system will never reach undesired states. In this paper, we propose a methodology for synthesizing such certificates for quantum circuits using a scenario-based approach, for both finite and infinite time horizons. In addition, our approach can handle uncertainty in the initial states and in the system's dynamics. We present several case studies on quantum circuits, comparing the performance of different types of barrier certificate and analyzing which one is most suitable for each case.

Problem

• Verifying quantum circuits using barrier certificates
• Handling uncertainty in initial states and dynamics
• Comparing barrier certificate types for suitability

Innovation

• Scenario-based barrier certificates synthesis
• Handles initial state and dynamics uncertainty
• Compares barrier certificates for quantum circuits