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arXiv:2109.07910

Quantum Algorithms in IBMQ Experience: Deutsch-Jozsa algorithm

Antônio Nonato de Oliveira, Estêvão V. B. de Oliveira, Alan C. Santos, Celso J. Villas-Bôas

Published Sep 15, 2021• 2 citations
arXivHTMLPDF

Abstract

Quantum information processing has been one of the pillars of the new information age. In this sense, the control and processing of quantum information plays a fundamental role, and computers capable of manipulating such information have become a reality. In this article we didactically present basic elements of the latest version of IBM's quantum computer and its main tools. We also present in detail the Deutsch-Jozsa algorithm used to differentiate constant functions from balanced functions, also, including a discussion of its efficiency against classical algorithms for the same task. The experimental implementation of the algorithm in a 4-qbit system is presented. Our article paves the way for a series of didactic investigations into the IBM system as well as the best known quantum algorithms.

DOI
10.48550/arxiv.2109.07910

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Quantum information processing has been one of the pillars of the new information age. In this sense, the control and processing of quantum information plays a fundamental role, and computers capable of manipulating such information have become a reality. In this article we didactically present basic elements of the latest version of IBM's quantum computer and its main tools. We also present in detail the Deutsch-Jozsa algorithm used to differentiate constant functions from balanced functions, also, including a discussion of its efficiency against classical algorithms for the same task. The experimental implementation of the algorithm in a 4-qbit system is presented. Our article paves the way for a series of didactic investigations into the IBM system as well as the best known quantum algorithms.
In this paper, we briefly review the basic concepts of quantum computation, entanglement, quantum cryptography and quantum fourier transform. Quantum algorithms like Deutsch Jozsa, Shor’s factorization and Grover’s data search are developed using fourier transform and quantum computation concepts to build quantum computers. Researchers are finding a way to build quantum computer that works more efficiently than classical computer. Among the standard well known algorithms in the field of quantum computation and communication we describe mathematically Deutsch Jozsa algorithm in detail for 2 and 3 qubits. Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.
Processamento de informação quântica tem sido um dos pilares da nova era da informação. Nessa direção, o controle e processamento de informação quântica desempenha um papel fundamental, e computadores capazes de manipular tais informações tem se tornado realidade. Neste artigo nós apresentamos, de forma didática, elementos básicos da versão mais recente do computador quântico da IBM e suas ferramentas. Nós ainda apresentamos em detalhes o algoritmo de Deutsch-Jozsa usado para diferenciar funções constantes de funções balanceadas, incluindo uma discussão de sua eficiência frente aos algoritmos clássicos para a mesma tarefa. A implementação experimental do algoritmo em um sistema de 4 qbits é apresentada. Nosso artigo abre caminho para uma série de investigações didáticas sobre o sistema da IBM, bem como os algoritmos quânticos mais conhecidos.
In quantum computers a unitary transformation is applied to a given initial state of a set of qubits through several quantum gates. Tests were conducted using Grover's algorithm and implemented in a variety of different ways on the publically available IBM quantum computers. Essentially, quantum computers manipulate quantum states instead of classical bits. Quantum information can be represented by the elementary units called quantum bits abbreviated as qubits or qbits. This chapter discusses the fundamental properties of quantum systems that are relevant to information processing. Quantum computation needs something much more than that quantum parallelism to be useful. This is achieved in Deutsch's algorithm which combines quantum parallelism with interference. One can simulate a classical circuit using a quantum circuit. That is, it is possible to perform classical computations on quantum computers. But the advantage of quantum computing is that powerful functions may be computed by making use of quantum parallelism, the fundamental feature of many quantum algorithms.
One of the most important quantum algorithms is Dutsch-Jozsa algorithm. It is one of the most basic ways to demonstrate the power of quantum computation. In this research a system consists of three electron (fermions) in state |0˃ and one in state |1˃ the Hadamard transform was applied on all states. Then, the black box is applied to compute f. Finally it has been applied the Hadamard gate. It was proved this quantum information processing system can solve Deutsch’s problem with one evaluation of the function f while the classical system requires (2 n /2 + 1 = 5) evaluations.
Abstract In the field of quantum computing, the Deutsch–Jozsa problem serves as a classical example illustrating the computational advantages of quantum algorithms over classical counterparts in specific scenarios. The problem involves efficiently determining the nature of a multi-valued function, showcasing how quantum parallelism can accelerate problem-solving. The Deutsch–Jozsa algorithm provides a framework for exploring these quantum advantages and offers insights into optimization tasks such as the minimum spanning tree (MST) problem in network design. Applications include network engineering, routing optimization, and resource allocation, where quantum-enhanced approaches can potentially outperform classical methods. This study examines the implementation of the Deutsch–Jozsa algorithm on quantum simulators and its adaptation in quantum versions of classical MST algorithms, such as the Ambainis–Spalek quantum variant of Edmonds–Karp. The analysis highlights the role of Grover’s search as a foundational component, integrating it with quantum MST techniques. Practical simulations using IBM Quantum platforms illustrate the algorithm’s potential for network optimization and broader information security applications.