An overview of quantum computation models: quantum automata

Abstract

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.

State succinctness of two-way finite automata with quantum and classical states

“…In the first part of this section we formally recall the model of 2QCFA we will use. Concerning the basics of quantum computation we refer the reader to [13,25], and concerning the basic properties of automata models, we refer the reader to [13,14,15,27,29,32].…”

Duality quantum computing

“…It is also interesting to investigate duality quantum computing from basic computing theories of quantum computers which has been reviewed extensively in Ref. [25] .…”

Two-Tape Finite Automata with Quantum and Classical States

“…As a quantum variant of FA, QFA have attracted wide attentions in the academic community [2,3,4,5,6,7,8,9]. Many kinds of QFA have been proposed and studied(e.g., see [13]). QFA are mainly divided into two kinds: one-way quantum finite automata (1QFA) and two-way quantum finite automata (2QFA).…”