International Conference on Computing and Emerging Sciences

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

Ali Al-Bayaty, Ali Al-Shuwaili, A H Alzubaidi, Marek A. Perkowski

Published Feb 4, 2026• 1 citation

Abstract

Conventionally, the quantum oracular algorithms, such as Deutsch-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 \(\sqrt {\rm{X}}\) gates. In quantum computing, the Hadamard and \(\sqrt {\rm{X}}\) gates create uniform superposition states of a qubit on the X-axis 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 \(\sqrt {\rm{X}}\) gates has been minimized to approximately 64% than the circuit of Grover's algorithm using Hadamard gates. Experimentally, because of the \(\sqrt {\rm{X}}\) is an IBM native gate, it has been proven that the final transpiled circuit of Grover's algorithm using \(\sqrt {\rm{X}}\) 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.

DOI: 10.1145/3797491.3797543

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