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Herald of Omsk University

Implementation of the Deutsch-Jozsa algorithm on an IBM quantum Computer

Sergeicheva, Skvortsov, Hismatov, Vakilov

Published Jun 10, 2025• 0 citations
Publisher

Abstract

The Deutsch-Jozsa algorithm has been implemented using the Qiskit software development kit and the IBM Quantum Lab. The accuracy of the algorithm is analyzed depending on the number of qubits and the results obtained on a real quantum computer and an emulator are compared.
DOI
10.24147/1812-3996.2025.2.22-28

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In the past few years, IBM has expanded their Quantum Experience to include a high-level Python module called Qiskit as well as a 15-qubit machine (ibmq_16_melbourne). In order to evaluate IBM’s progress, we create an overview of the processes involved in developing and running an algorithm on IBM’s quantum machines. This includes exploring the new resources that IBM has made available recently including the Qiskit Python module. Then, we test textbook algorithms such as the Deutsch-Jozsa algorithm, Grover’s search algorithm, and Quantum Fourier Transform on ibmq_16_melbourne and compare the results with the output of a simulator. Constraints imposed by IBM’s Quantum Experience and significant differences between algorithm performance on IBM's quantum hardware and the simulator will be used to assess IBM’s quantum computing capabilities.
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.
The quantum computing is a giant leap forward in comparison with our common computer models as it allows us to solve some problems with a much smaller number of steps. In this paper, we will demonstrate the design, development, and testing of the DeutschJozsa quantum algorithm using Qiskit. The algorithm can determine whether a Boolean function is identical or evenly divides with a single special query where traditional algorithms may require as many as 2n -1 +1 checks in the worst-case. We simulated the algorithm on an ideal simulator (Qiskit Aer) and IBM Quantum real hardware. Three aspects that we examined were the measurement accuracy, the depth of the quantum circuit, and how the noise of the real world, including decoherence and gate errors as well as readout errors, would influence the outcome of the NISQ devices. The simulator has nearly excellent precision, whereas the actual hardware has some visible disparities due to noise. These findings verify a undeniable quantum efficiency in query complexity and the cost decreases to a constant cost of O(1) quantum versus an exponential cost of O(2n) using a classical computer. Altogether, this paper is an example of quantum parallelism and quantum interference in a practical sense and serves as a good reference point to the capabilities of the current quantum hardware.