An Interpretation of Bunched Logic for Reasoning about Heap-Manipulating Quantum Programs

Abstract:We introduce heap manipulation into quantum programming languages to enable flexible quantum memory management, which in turn poses new challenges for reasoning about program correctness. To address these challenges, we develop a novel quantum interpretation of bunched logic by extending Birkhoff--von Neumann quantum logic to Hilbert spaces whose dimensions vary to accommodate the dynamic allocation and deallocation of variables on the quantum heap. Beyond the separating conjunction ($*$), we present, for the first time, a quantum interpretation of the separating implication ($-\mkern-3mu*$) to support backward reasoning. This interpretation preserves the adjunction between ($*$) and ($-\mkern-3mu*$), ensuring that both operators capture spatial properties and are precisely aligned with the semantics of quantum heap manipulations. Building on this foundation, we establish a quantum separation logic that supports local reasoning and is relatively complete.

arXiv:2409.10153 [quant-ph]

(or arXiv:2409.10153v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2409.10153 Focus to learn more arXiv-issued DOI via DataCite

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