A Practical Quantum Hoare Logic with Classical Variables, I

2024-12-13

arXiv.org

AI Summary

Verifying quantum programs with classical variables remains challenging due to high conceptual barriers, lack of integration with classical verification toolchains, and insufficient logical foundations. Method: This paper proposes a lightweight Hoare-style logic framework. It introduces parameterized quantum gates and quantum arrays into quantum Hoare logic with classical variables—the first such extension. It designs novel measurement inference rules ensuring minimal compatibility with classical first-order Hoare logic. Specifications adopt a two-layer structure: classical first-order formulas augmented with parameterized quantum predicates, enabling semantically precise and intuitive assertion expression. Contribution/Results: The framework enables seamless reuse of classical verification tools, drastically reducing learning and adoption costs. It supports expressive, compositional, and mathematically rigorous correctness proofs for quantum programs, thereby advancing the practical engineering of quantum software.

Technology Category

Machine Learning: Quantum Machine LearningKnowledge Representation and Reasoning: Logic ProgrammingConstraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

Security and Privacy: Data transparency and provenanceSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsGraph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic applies to quantum programs with classical variables that incorporate quantum arrays and parameterised quantum gates, which have not been addressed in previous research on quantum Hoare logic, either with or without classical variables. (2) Intuitive correctness specifications: In our logic, preconditions and postconditions for quantum programs with classical variables are specified as a pair consisting of a classical first-order logical formula and a quantum predicate formula (possibly parameterised by classical variables). These specifications offer greater clarity and align more closely with the programmer's intuitive understanding of quantum and classical interactions. (3) Simplified proof system: By introducing a novel idea in formulating a proof rule for reasoning about quantum measurements, along with (2), we develop a proof system for quantum programs that requires only minimal modifications to classical Hoare logic. Furthermore, this proof system can be effectively and conveniently combined with classical first-order logic to verify quantum programs with classical variables. As a result, the learning curve for quantum program verification techniques is significantly reduced for those already familiar with classical program verification techniques, and existing tools for verifying classical programs can be more easily adapted for quantum program verification.

Problem

• Develops Hoare-style logic for quantum programs with classical variables
• Enhances expressivity with quantum arrays and parameterised gates
• Simplifies proof system by integrating classical Hoare logic

Innovation

• Enhanced expressivity with quantum arrays
• Intuitive classical-quantum correctness specifications
• Simplified proof system for measurements