An Axiomatization for Quantum Processes to Unifying Quantum and Classical Computing

Abstract: We establish an axiomatization for quantum processes, which is a quantum generalization of process algebra ACP (Algebra of Communicating Processes). We use the framework of a quantum process configuration $\langle p, \varrho\rangle$, but we treat it as two relative independent part: the structural part $p$ and the quantum part $\varrho$, because the establishment of a sound and complete theory is dependent on the structural properties of the structural part $p$. We let the quantum part $\varrho$ be the outcomes of execution of $p$ to examine and observe the function of the basic theory of quantum mechanics. We establish not only a strong bisimularity for quantum processes, but also a weak bisimularity to model the silent step and abstract internal computations in quantum processes. The relationship between quantum bisimularity and classical bisimularity is established, which makes an axiomatization of quantum processes possible. An axiomatization for quantum processes called qACP is designed, which involves not only quantum information, but also classical information and unifies quantum computing and classical computing. qACP can be used easily and widely for verification of most quantum communication protocols.