Towards the Notion of an Abstract Quantum Automaton
Mizal Alobaidi (1), Andriy Batyiv (2), Grygoriy Zholtkevych (2) ((1), Tikrit University, Faculty of Computer Sciences, Mathematics, (2) V.N., Karazin Kharkiv National University, School of Mathematics)

TL;DR
This paper develops a rigorous mathematical framework for quantum information processing systems by extending classical state machines to include quantum operations, exemplified through modeling quantum teleportation as an abstract quantum automaton.
Contribution
It introduces the concept of an abstract quantum automaton, generalizing classical models with quantum memory and operations for quantum information processing.
Findings
Quantum teleportation modeled as an evolutionary process of an abstract quantum automaton.
Framework provides a rigorous mathematical description of quantum information processing systems.
Extension of classical state machines to include quantum memory and operations.
Abstract
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines is refined by introducing constrains on a state structure, namely, it is assumed that state of computational process has two components: a control unit state and a memory state. Then authors modify the class of models by substituting the deterministic evolutionary mechanism for a stochastic evolutionary mechanism. This approach can be generalized to the quantum case: one can replace transformations of a classical memory with quantum operations on a quantum memory. Hence the authors come to the need to construct a mathematical model of an operation on the quantum memory. It leads them to the notion of an abstract quantum automaton. Further the authors…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
