BI-based Reasoning about Quantum Programs with Heap Manipulations

• URL: http://arxiv.org/abs/2409.10153v1
• Date: Mon, 16 Sep 2024 10:34:45 GMT
• Title: BI-based Reasoning about Quantum Programs with Heap Manipulations
• Authors: Bonan Su, Li Zhou, Yuan Feng, Mingsheng Ying,
• Abstract summary: We provide well-founded semantics for a quantum programming language Qwhile-hp with heap manipulations. We develop a quantum BI-style logic that includes interpretations for separating implication. We then adopt this quantum BI-style logic as an assertion language to reason about heap-manipulated quantum programs.
• Score: 5.744265100221585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide well-founded semantics for a quantum programming language Qwhile-hp with heap manipulations, where allocation statements follow a dirty pattern, meaning that newly allocated qubits can nondeterministically assume arbitrary initial states. To thoroughly characterize heap manipulations in the quantum setting, we develop a quantum BI-style logic that includes interpretations for separating implication ($-\mkern-3mu*$) and separating conjunction ($*$). We then adopt this quantum BI-style logic as an assertion language to reason about heap-manipulated quantum programs and present a quantum separation logic which is sound and relatively complete. Finally, we apply our framework to verify the correctness of various practical quantum programs and to prove the correct usage of dirty ancilla qubits.

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