Formalizing the Semantics of a Classical-Quantum Imperative Language in Coq
-
Published:2023-10-27
Issue:
Volume:
Page:
-
ISSN:0218-1266
-
Container-title:Journal of Circuits, Systems and Computers
-
language:en
-
Short-container-title:J CIRCUIT SYST COMP
Author:
Shi Wenjun1ORCID,
Cao Qinxiang2ORCID,
Deng Yuxin1ORCID
Affiliation:
1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 3663 North Zhongshan Road, Shanghai 200062, P. R. China
2. John Hopcroft Center of Computer Science, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, P. R. China
Abstract
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Project funded by China Postdoctoral Science Foundation
Fundamental Research Funds for the Central Universities
National Key Research and Development Program of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Electrical and Electronic Engineering,Hardware and Architecture,Electrical and Electronic Engineering,Hardware and Architecture