An Axiomatization for Quantum Processes to Unifying Quantum and Classical Computing

摘要

We establish an axiomatization for quantum processes, which is a quantumgeneralization of process algebra ACP (Algebra of Communicating Processes). Weuse the framework of a quantum process configuration $langle p,arrhoangle$, but we treat it as two relative independent part: thestructural part $p$ and the quantum part $arrho$, because the establishmentof a sound and complete theory is dependent on the structural properties of thestructural part $p$. We let the quantum part $arrho$ be the outcomes ofexecution of $p$ to examine and observe the function of the basic theory ofquantum mechanics. We establish not only a strong bisimularity for quantumprocesses, but also a weak bisimularity to model the silent step and abstractinternal computations in quantum processes. The relationship between quantumbisimularity and classical bisimularity is established, which makes anaxiomatization of quantum processes possible. An axiomatization for quantumprocesses called qACP is designed, which involves not only quantum information,but also classical information and unifies quantum computing and classicalcomputing. qACP can be used easily and widely for verification of most quantumcommunication protocols.