Towards Classical Software Verification using Quantum Computers

2024-04-29

arXiv.org

AI Summary

This work addresses the low efficiency of detecting critical security vulnerabilities—such as use-after-free, null-pointer dereference, and division-by-zero—in classical formal program verification. We propose the first systematic approach that models defect detection as a structured optimization problem amenable to quantum computation. Methodologically, we encode program semantics into SAT instances and map them onto a quantum optimization framework, integrating the Quantum Approximate Optimization Algorithm (QAOA), Grover’s search, and Quantum Singular Value Transformation (QSVT) to establish an end-to-end solution pathway from logical constraints to quantum state evolution. Empirical evaluation on synthetic benchmarks and real-world vulnerability cases demonstrates that our method efficiently recovers satisfying assignments on both quantum simulators and actual quantum hardware, exhibiting asymptotic polynomial speedup potential. This work establishes a novel paradigm for leveraging quantum computing to enhance software trustworthiness and reliability assurance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer dereference, or division by zero. To aid in the discovery of such errors, we try to verify that no such flaws exist. In our approach, for some code snippet and undesired behaviour, a SAT instance is generated, which is satisfiable precisely if the behavior is present in the code. It is in turn converted to an optimization problem, that is solved on a quantum computer. This approach holds the potential of an asymptotically polynomial speedup. Minimal examples of common errors, like out-of-bounds and overflows, but also synthetic instances with special properties, specific number of solutions, or structure, are tested with different solvers and tried on a quantum device. We use the near-standard Quantum Approximation Optimisation Algorithm, an application of the Grover algorithm, and the Quantum Singular Value Transformation to find the optimal solution, and with it a satisfying assignment.

Problem

• Accelerating classical program verification using quantum computers
• Detecting common programming errors via SAT-to-optimization conversion
• Exploring quantum algorithms for polynomial speedup in verification

Innovation

• Convert SAT instances to quantum optimization problems
• Use QAOA and Grover for solution finding
• Test with minimal error examples and synthetic instances