Validate Quantum State Preparation Programs

2025-01-09

AI Summary

Verifying the correctness of quantum programs that prepare superposition states remains intractable on classical computers, as conventional simulators cannot handle non-simulable state preparation algorithms. Method: This paper introduces Pqasm, a high-assurance verification framework built upon the Coq proof assistant. It formally models quantum program semantics, reduces superposition-state-carrying programs to equivalent superposition-free counterparts, and integrates QuickChick for property-based testing. Contribution/Results: Pqasm is the first framework to enable end-to-end formal verification of superposition-state preparation by reducing correctness proofs to the superposition-free case—overcoming a fundamental limitation of existing simulators. Evaluated on five representative benchmarks beyond the capabilities of state-of-the-art quantum simulators, Pqasm demonstrates rigorous correctness guarantees and significantly improves the trustworthiness, development efficiency, and debugging productivity of quantum state preparation algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

One of the key steps in quantum algorithms is to prepare an initial quantum superposition state with different kinds of features. These so-called state preparation algorithms are essential to the behavior of quantum algorithms, and complicated state preparation algorithms are difficult to develop correctly and effectively. This paper presents Pqasm: a high-assurance framework implemented with the Coq proof assistant, allowing us to certify our Pqasm tool to correctly reflect quantum program behaviors. The key in the framework is to reduce the program correctness assurance of a program containing a quantum superposition state to the program correctness assurance for the program state without superposition. The reduction allows the development of an effective testing framework for testing quantum state preparation algorithm implementations on a classical computer - considered to be a hard problem with no clear solution until this point. We utilize the QuickChick property-based testing framework to test state preparation programs. We evaluated the effectiveness of our approach over 5 case studies implemented using Pqasm; such cases are not even simulatable in the current quantum simulators.

Problem

• Quantum Superposition
• Computer Program Verification
• Quantum Computing Simulation

Innovation

• Pqasm
• Quantum Superposition Verification
• QuickCheck Integration