🤖 AI Summary
Efficiently identifying qubit entanglement in quantum programs is critical for circuit optimization and correctness verification, yet exact analysis suffers from exponential time complexity. This paper introduces the first static entanglement analysis framework based on abstract interpretation: it extends classical abstract interpretation by designing a quantum-state-specific abstract domain and corresponding transfer functions, and develops a linear-time approximate analysis algorithm. Implemented as a prototype in Standard ML, the system safely and efficiently determines potential entanglement between any pair of qubits—without incurring exponential overhead. The approach ensures both strong scalability and theoretical soundness, providing provably safe over-approximations. It constitutes the first systematic application of approximation-based program analysis techniques to quantum entanglement prediction, establishing a verifiable foundation for static analysis in quantum software engineering.
📝 Abstract
Entanglement is a fundamental property of quantum systems, essential for non-trivial quantum programs. Identifying when qubits become entangled is critical for circuit optimization, and for arguing for the correctness of quantum algorithms. This paper presents a static analysis method for approximating entanglement by extending an already existing abstract interpretation, thus avoiding the exponential slowdown of an exact analysis. The approach is shown to be sound and an implementation is provided in Standard ML with linear-time scalability.