Quantum Representation for Deterministic Pushdown Automata

Abstract

There are many papers presenting quantum computing models. The definitions parallel the classical definitions of finite state automata, push down automata, context-free grammars etc. Classical computing model definitions define languages precisely. We can state that a string belongs to a language or does not belong to it with no room for error. Quantum definitions do not possess this certainty. Sacrificing the certainty and adopting a quantum definition of a computing model does not appear to provide any concrete power to the model. Therefore, the path of this paper is to begin from the classical definition and end in a quantum circuit. In this paper we start from a Deterministic Push-Down Automaton (DPDA). We present circuit for state transition and stack operations. The circuits presented can be viewed as independent algorithms. As an example, the approach used to construct the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix.