Translation of Quantum Circuits into Quantum Turing Machines for Deutsch and Deutsch-Jozsa Problems

TL;DR

This paper demonstrates how Quantum Turing Machines can be used to represent and analyze Deutsch and Deutsch-Jozsa algorithms, highlighting their equivalence to quantum circuits and illustrating quantum features from a Turing machine perspective.

Contribution

It introduces a translation strategy from quantum circuits to Quantum Turing Machines using well-known algorithms, enhancing understanding of quantum computing models.

Findings

QTM and quantum circuit models are equivalent for these algorithms

Superposition can be illustrated from a QTM perspective

Translation strategy aids in high-level quantum computing education

Abstract

We want in this article to show the usefulness of Quantum Turing Machine (QTM) in a high-level didactic context as well as in theoretical studies. We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms. Further we introduce a strategy of translation from Quantum Circuit to Quantum Turing models by these examples. Moreover we illustrate some features of Quantum Computing such as superposition from a QTM point of view and starting with few simple examples very known in Quantum Circuit form.