A Quantum interpretation of separating conjunction for local reasoning of Quantum programs based on separation logic

• Main Authors: LE, Xuan Bach, LIN, Shang-Wei, SUN, Jun, SANAN, David
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Formal Semantics; Quantum Computing; Verification; Software Engineering; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/6941; https://ink.library.smu.edu.sg/context/sis_research/article/7944/viewcontent/3498697_pvoa.pdf
• Institution: Singapore Management University

It is well-known that quantum programs are not only complicated to design but also challenging to verify because the quantum states can have exponential size and require sophisticated mathematics to encode and manipulate. To tackle the state-space explosion problem for quantum reasoning, we propose a Hoare-style inference framework that supports local reasoning for quantum programs. By providing a quantum interpretation of the separating conjunction, we are able to infuse separation logic into our framework and apply local reasoning using a quantum frame rule that is similar to the classical frame rule. For evaluation, we apply our framework to verify various quantum programs including Deutsch–Jozsa’s algorithm and Grover's algorithm.