RapunSL: Untangling Quantum Computing with Separation, Linear Combination and Mixing
Yusuke Matsushita, Kengo Hirata, Ryo Wakizaka, Emanuele D'Osualdo
TL;DR
RapunSL addresses the scalability gap in quantum program verification by unifying three locality notions—entanglement-locality, basis-locality, and outcome-locality—into a single logic. It introduces a mixed-state assertion language with three connectives: separation, sum, and mixing (tagged mixing), enabling modular reasoning about both superpositions and measurement-induced mixtures. The authors develop a sound program logic with well-behaved frameability and abstraction, and validate it across case studies including Toffoli-based dirty qubits, quantum teleportation, lattice-surgery CNOT, and standard quantum error-correcting codes. The framework supports automated reasoning patterns and offers a pathway to density-matrix encodings when state explosion becomes prohibitive, making RapunSL a practical tool for scalable quantum program verification and modular design of quantum circuits and protocols.
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.