Quantum Pushdown Automata with Garbage Tape

Several kinds of quantum pushdown automata models have been proposed, and their computational power has been investigated intensively. However, for some quantum pushdown automaton models, it is unknown whether quantum models are at least as powerful as their classical counterparts or not. This is due to the reversibility restriction. In this paper, we introduce a new quantum pushdown automaton model that has a garbage tape. This model can overcome the reversibility restriction by exploiting the garbage tape to store popped symbols. We show that the proposed model can simulate any quantum pushdown automaton with classical stack as well as any probabilistic pushdown automaton. We also show that our model can solve a certain promise problem exactly while deterministic pushdown automata cannot. These results imply that our model is strictly more powerful than its classical counterparts in the setting of exact, one-sided error and non-deterministic computation. Showing impossibility for a promise problem is a difficult task in general. However, by analyzing the behavior of a deterministic pushdown automaton carefully, we obtained the impossibility result. This is one of the main contributions of the paper.