Coq中经典量子命令式语言语义的形式化

IF 0.9 4区工程技术 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Journal of Circuits Systems and Computers Pub Date : 2023-10-27 DOI:10.1142/s0218126624501123

Wenjun Shi, Qinxiang Cao, Yuxin Deng

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引用次数: 0

摘要

为了验证量子电路或算法的功能正确性，一个突出的方法是将它们指定为量子程序，并在定理证明器中半自动地推导它们。首先形式化基本量子语言的语义是必不可少的。我们在Coq中形式化了一种命令式语言，它允许经典和量子信息交互。我们定义了小步操作语义和基于状态的指称语义。然后证明了这两个语义之间的一致性定理。还定义了基于分布的指示语义，并与基于状态的指示语义相关联。最后，我们描述了几种典型的量子算法，并利用基于分布的指称语义验证了它们的正确性。

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Formalizing the Semantics of a Classical-Quantum Imperative Language in Coq

In order to verify the functional correctness of quantum circuits or algorithms, a prominent approach is to specify them as quantum programs and semi-automatically deduce them in a theorem prover. It is indispensable to first formalize the semantics of the basic quantum language. We formalize in Coq an imperative language which allows for classical and quantum information interactions. We define small-step operational semantics and state-based denotational semantics. Then we prove a consistency theorem between these two semantics. A distribution-based denotational semantics is also defined and related to the state-based one. Finally, we describe a few typical quantum algorithms and utilize the distribution-based denotational semantics to verify their correctness.

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来源期刊

Journal of Circuits Systems and Computers 工程技术-工程：电子与电气

CiteScore

2.80

自引率

26.70%

发文量

350

审稿时长

5.4 months

期刊介绍： Journal of Circuits, Systems, and Computers covers a wide scope, ranging from mathematical foundations to practical engineering design in the general areas of circuits, systems, and computers with focus on their circuit aspects. Although primary emphasis will be on research papers, survey, expository and tutorial papers are also welcome. The journal consists of two sections: Papers - Contributions in this section may be of a research or tutorial nature. Research papers must be original and must not duplicate descriptions or derivations available elsewhere. The author should limit paper length whenever this can be done without impairing quality. Letters - This section provides a vehicle for speedy publication of new results and information of current interest in circuits, systems, and computers. Focus will be directed to practical design- and applications-oriented contributions, but publication in this section will not be restricted to this material. These letters are to concentrate on reporting the results obtained, their significance and the conclusions, while including only the minimum of supporting details required to understand the contribution. Publication of a manuscript in this manner does not preclude a later publication with a fully developed version.