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International Scientific Conference Sinteza

Quantum Computers - Example of Executing the Deutsch Quantum Algorithm Using Google Colab

Željko Eremić, Tanja Sekulić, Iris Borjanović Trusina

Published Jan 1, 2026• 0 citations
Publisher

Abstract

In this paper, an introduction to the basic principles of quantum computing is provided, from concepts of quantum mechanics to their mathematical and computational representation.The core phenomena of quantum mechanics, such as superposition, interference, and entanglement, are explained, and their applications in quantum information processing are described.Mathematical representation of quantum information, starting from qubits, quantum gates, and quantum operations, is presented and explained.Also, the overview of basic quantum algorithms is given and compared to classical approaches.The quantum Deutsch algorithm is presented and discussed mathematically.Prerequisites and programming code in Python for executing the quantum Deutsch's algorithm are presented.Figures of quantum circuits and execution results are given.Finally, the results of the execution of this algorithm are discussed.

DOI
10.15308/sinteza-2026-334-339

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In this paper, an introduction to the basic principles of quantum computing is provided, from concepts of quantum mechanics to their mathematical and computational representation.The core phenomena of quantum mechanics, such as superposition, interference, and entanglement, are explained, and their applications in quantum information processing are described.Mathematical representation of quantum information, starting from qubits, quantum gates, and quantum operations, is presented and explained.Also, the overview of basic quantum algorithms is given and compared to classical approaches.The quantum Deutsch algorithm is presented and discussed mathematically.Prerequisites and programming code in Python for executing the quantum Deutsch's algorithm are presented.Figures of quantum circuits and execution results are given.Finally, the results of the execution of this algorithm are discussed.
Quantum computing uses quantum-mechanical principles to enable new models of computation bexond the classical paradigm. This article presents an accessible introduction to the mathematical and conceptual foundations of quantum computing, covering qubits, quantum gates, multi-qubit systems, entanglement, and measurement. The gate-based computation model and quantum circuits are introduced, together with key notations such as universality and reversibility. As an illustrative example, the Deutsch-Josza algorithm is discussed to demonstrate how quantum algorithm can be constucted. The article concludes with a brief overview of the current state and challenges of quantum computing.
A quantum computer is a machine that exploits quantum phenomena to store information and perform computations.\nThe chief goal of this article is to provide a brief but comprehensive introduction to quantum computing. It overviews some mathematical underpinnings of quantum computation for readers with only a basic knowledge of linear algebra and probability. However, it does not attempt to be exhaustive nor make an exposition of quantum physics. It further does not attempt to stay current with physical implementations of quantum computers.\nAfter providing a brief historical background, the article introduces the notion of a quantum bit (qubit) and the linear operators (gates) that act on these. It then addresses systems of multiple qubits and their corresponding gates. Along the way, the article covers the essential concepts of separable systems, as well quantum interference and decoherence. It also describes how to represent gates as quantum circuits. To conclude, it explains the underpinnings of two simple but insightful quantum algorithms. A final section suggests further readings for those who wish to delve deeper into quantum computing.
This chapter provides an introduction to the principles of quantum information processing, establishing the theoretical foundation for quantum machine learning. It covers the representation of quantum states using qubits, the mathematical framework of quantum mechanics, and the role of superposition, entanglement, and measurement. Key models such as quantum circuits and quantum gates are introduced, along with illustrative algorithms including Deutsch–Jozsa and Grover’s search. These examples demonstrate how quantum mechanics enables computational speedups and highlights the potential advantages of quantum computing in learning and optimization tasks.
This paper investigates the core principles of quantum computation, providing an in-depth understanding of quantum phenomena and illustrating how these principles form the scientific foundation of the field. The pivotal physical concepts, such as properties of subatomic particles, including electrons and photons, as well as their mathematical description through linear algebra are examined. It focuses on the qubit, the quantum analogue of a classical bit, featuring properties like superposition, entanglement, and wave function collapse, which redefine the traditional concept of information processing. The mathematical structures that underlie quantum system modelling—vector spaces, tensor products, and Dirac notation—are also systematically explained. Essential components of quantum computation involve logic gates such as Pauli matrices and Hadamard gates, which demonstrate the novel application of qubits in unique ways. This sets up an important theme of the interdependence and potential for transformation of quantum states through the illustration of advanced ideas of quantum entanglement and teleportation. Quantum circuits serve as an outstanding example of how reversibility and superposition are exploited to solve complex problems at unprecedented levels of efficiency. The paper also highlights the Deutsch-Jozsa algorithm as a compelling example of quantum superiority over traditional computational approaches. Together, these findings emphasize the transformative potential of quantum computing for science and industry.
The main goal of this thesis is to give information on quantum computer principles and its latest development. In the first part we introduce quantum bits, quantum registers and quantum gates. We show basic operations acting on one and more qubits. On an example we present, how it is possible to construct an arbitrary gate using only elementary quantum gates. We describe a behaviour of quantum computers called quantum parallelism and show its application in Deutsch's algorithm. We define the quantum Fourier transform and its applications. In the last chapter we explain on what principle the D-Wave quantum computer works. In this thesis we compare classical and quantum computers in terms of algorithms and computational speed.