Improving the Circuit Realization of Grover’s Quantum Search Algorithm by Replacing Hadamard with √ × Gates

Authors

• Ali Al-Bayaty, Portland State UniversityFollow
• Ali Al-Shuwaili, University of Information Technology and Communications, College of Engineering, Baghdad, Iraq
• Abbas AlZubaidi, American University of Iraq-Baghdad, College of Healthcare Technologies, Baghdad, Iraq
• Marek Perkowski, Portland State UniversityFollow

Published In

Icces 2026 Conference Proceedings of 2026 the 2nd International Conference Computing and Emerging Sciences

Document Type

Conference Proceeding

Publication Date

4-20-2026

Subjects

Computer science, Information storage and retrieval systems

Abstract

Jozsa, Bernstein-Vazirani, and Grover, utilize Hadamard gates to create uniform superposition states for the input qubits of an oracle. However, Hadamard gates are non-native (non-supported) gates in all real quantum computers. For this reason, Hadamard gates are considered cost-expensive gates when realizing (transpiling) such algorithms into a real quantum computer. This paper introduces a new methodology for cost-effective transpilation of Grover’s algorithm into real quantum computers, by replacing all Hadamard gates with √ X gates. In quantum computing, the Hadamard and √ X gates create uniform superposition states of a qubit on the Xaxis and Y-axis of the Bloch sphere, respectively. Hence, we utilize a different axis of the Bloch sphere to construct a cost-effective realization for the final transpiled circuit of Grover’s algorithm. Theoretically, the final transpiled circuit of Grover’s algorithm using √ X gates has been minimized to approximately 64% than the circuit of Grover’s algorithm using Hadamard gates. Experimentally, because of the √ X is an IBM native gate, it has been proven that the final transpiled circuit of Grover’s algorithm using √ X gates always has a lower quantum cost of 6% than the circuit of Grover’s algorithm using Hadamard gates, due to the limited layout (architecture) connectivity of the physical neighboring qubits for IBM quantum computers.

Rights

Copyright (c) 2026 The Authors

This work is licensed under a Creative Commons Attribution 4.0 International License.

Locate the Document

https://doi.org/10.1145/3797491.3797543

DOI

10.1145/3797491.3797543

Persistent Identifier

https://archives.pdx.edu/ds/psu/44702

Citation Details

Al-Bayaty, A., Al-Shuwaili, A., AlZubaidi, A., & Perkowski, M. (2026). Improving the Circuit Realization of Grover’s Quantum Search Algorithm by Replacing Hadamard with √X Gates. In (Editor), Proceedings of the 2026 2nd International Conference on Computing and Emerging Sciences.