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arXiv:1507.03344

Reversible Quantum Process Algebra with Guards

Yong Wang

Published Jul 13, 2015• 0 citations
arXivHTMLPDF

Abstract

Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, $π_{tc}$ to $π$ calculus, APPTC to probabilistic process algebra. And we also did some work on reversible process algebra and probabilistic truly concurrent process algebra. In this book, we utilize reversible truly concurrent process algebras APRTC and probabilistic process algebra APPTC to model quantum computing and unify quantum and classical computing.

DOI
10.48550/arxiv.1507.03344

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Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra. And we also did some work on reversible process algebra and probabilistic truly concurrent process algebra. In this book, we utilize reversible truly concurrent process algebras APRTC and probabilistic process algebra APPTC to model quantum computing and unify quantum and classical computing.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus , APPTC to probabilistic process algebra. And we also did some work on reversible process algebra and probabilistic truly concurrent process algebra. In this book, we utilize reversible truly concurrent process algebras APRTC and APPTC to model quantum computing and unify quantum and classical computing.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP,πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra.In this book, we utilize truly concurrent process algebras APTC and APPTC to model quantum computing and unify quantum and classical computing.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra. Now, it is the time to utilize truly concurrent process algebras APTC and APPTC to model quantum computing and unify quantum and classical computing. In this book, we introduce the preliminaries, the utilization of APTC to unify quantum and classical computing and its usage in verification of quantum communication protocols, the utilization of APPTC to unifying quantum and classical computing and its usage in verification of quantum communication protocols.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra, APTC with localities to process algebra with localities. In quantum process algebras, there are several well-known work, and we ever did some work to unify quantum and classical computing under the framework of ACP \cite{ACP} and probabilistic process algebra. Now, it is the time to utilize truly concurrent process algebras with localities to model quantum computing and unify quantum and classical computing in this book. Since this work is with localities, it is suitable to verify the distribution of quantum communication protocols.
Modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification. As a consequence, a general framework formally describing communication and concurrency in complex quantum systems is necessary. For this purpose, we propose a model named qCCS. It is a natural quantum extension of classical value-passing CCS which can deal with input and output of quantum states, and unitary transformations and measurements on quantum systems. The operational semantics of qCCS is given in terms of probabilistic labeled transition system. This semantics has many different features compared with the proposals in the available literature in order to describe the input and output of quantum systems which are possibly correlated with other components. Based on this operational semantics, the notions of strong probabilistic bisimulation and weak probabilistic bisimulation between quantum processes are introduced. Furthermore, some properties of these two probabilistic bisimulations, such as congruence under various combinators, are examined.