Towards the Notion of an Abstract Quantum Automaton

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 demonstrate that a quantum teleportation process is described as evolutionary process for some abstract quantum automaton.