Probabilistic Process Algebra to Unifying Quantum and Classical Computing in Closed Systems

TL;DR

This paper introduces a probabilistic process algebra framework called qACP that unifies quantum and classical computing in closed systems, enabling verification of mixed quantum-classical systems.

Contribution

It extends the existing open-system qACP to closed systems, providing an axiomatization for quantum and classical processes under closed-system assumptions.

Findings

Unified quantum and classical computing in closed systems.

Framework applicable for verifying quantum communication protocols.

Addresses probability in quantum process modeling.

Abstract

We have unified quantum and classical computing in open quantum systems called qACP which is a quantum generalization of process algebra ACP. But, an axiomatization for quantum and classical processes with an assumption of closed quantum systems is still missing. For closed quantum systems, unitary operator, quantum measurement and quantum entanglement are three basic components for quantum computing. This leads to probability unavoidable. Along the solution of qACP to unify quantum and classical computing in open quantum systems, we unify quantum and classical computing with an assumption of closed systems under the framework of ACP-like probabilistic process algebra. This unification make it can be used widely in verification for quantum and classical computing mixed systems, such as most quantum communication protocols.