A Quantum Interpretation of Bunched Logic & Quantum Separation Logic

We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quan...

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Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 14
Hlavní autoři: Zhou, Li, Barthe, Gilles, Hsu, Justin, Ying, Mingsheng, Yu, Nengkun
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
Cognition
Machine learning algorithms
Quantum algorithm
Quantum state
Semantics
Tutorials
Writing
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Abstract We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states-the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirq's tutorial on the Variational Quantum Algorithm (VQA).
AbstractList We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states-the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirq's tutorial on the Variational Quantum Algorithm (VQA).
Author Hsu, Justin
Barthe, Gilles
Zhou, Li
Yu, Nengkun
Ying, Mingsheng
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  givenname: Li
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  organization: Max Planck Institute for Security and Privacy
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  organization: University of Wisconsin-Madison
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  givenname: Mingsheng
  surname: Ying
  fullname: Ying, Mingsheng
  organization: University of Technology Sydney
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  givenname: Nengkun
  surname: Yu
  fullname: Yu, Nengkun
  organization: University of Technology Sydney
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Snippet We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating...
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SubjectTerms Cognition
Machine learning algorithms
Quantum algorithm
Quantum state
Semantics
Tutorials
Writing
Title A Quantum Interpretation of Bunched Logic & Quantum Separation Logic
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