On the Power of One-Sided Error Quantum Pushdown Automata with Classical Stack Operations

Abstract

One of important questions on quantum computing is whether there is a computational gap between the models that are allowed to use quantum effects and the models that are not. Several types of quantum computation models have been proposed, including quantum finite automata and quantum pushdown automata (with quantum pushdown stack). It has been shown that some quantum computation models are more powerful than classical counterparts and some are not since quantum computation models are required to obey some restrictions such as reversible state transitions. In this paper, we investigate the power of quantum pushdown automata whose stack is assumed to be implemented as a classical device, and show that they are strictly more powerful than classical counterparts in the one-sided error setting. That is, we show that there is a non-context-free language which quantum pushdown automata with classical stack operations can recognize with one-sided error.