RapunSL: Untangling Quantum Computing with Separation, Linear Combination and Mixing

2025-11-28

AI Summary

This paper addresses the scalability bottleneck in deductive reasoning for quantum programs arising from superposition and measurement-induced mixed states. We propose RapunSL, a novel quantum separation logic. Our method introduces two formal locality principles: *basis locality*, which reduces reasoning about superpositions to pure states, and *outcome locality*, which reduces reasoning about post-measurement mixed states to pure states. To capture quantum effects structurally, we extend separation logic with two new connectives—linear combination (for superposition) and probabilistic mixture (for measurement)—enabling compositional decomposition of quantum operations. RapunSL supports localized program reasoning and formal verification. Evaluated on multiple complex quantum algorithms—including Shor’s algorithm and quantum walk protocols—it demonstrates significant improvements in both reasoning efficiency and scalability. By unifying expressive power with practical verifiability, RapunSL establishes a foundational framework for scalable, rigorous quantum program verification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Quantum Separation Logic (QSL) has been proposed as an effective tool to improve the scalability of deductive reasoning for quantum programs. In QSL, separation is interpreted as disentanglement, and the frame rule brings a notion of entanglement-local specification (one that only talks about the qubits entangled with those acted upon by the program). In this paper, we identify two notions of locality unique to the quantum domain, and we construct a novel quantum separation logic, RapunSL, which is able to soundly reduce reasoning about superposition states to reasoning about pure states (basis-locality), and reasoning about mixed states arising from measurement to reasoning about pure states (outcome-locality). To do so, we introduce two connectives, linear combination and mixing, which together with separation provide a dramatic improvement in the scalability of reasoning, as we demonstrate on a series of challenging case studies.

Problem

• Improving scalability of deductive reasoning for quantum programs
• Reducing reasoning about superposition states to pure states
• Handling mixed states from measurement through pure state reasoning

Innovation

• Uses separation for disentanglement in quantum logic
• Introduces linear combination for superposition state reasoning
• Employs mixing for measurement outcome locality