Model-Checking Linear-Time Properties of Quantum Systems
  We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and omega-properties recognizable by reversible Buechi automata. 
Mingsheng Ying, Yangjia Li, Nengkun Yu and Yuan Feng
quant-ph