https://doi.org/10.1140/epjp/s13360-025-06518-3
Regular Article
An efficient implementation of a quantum search algorithm for arbitrary 
1
School of Arts and Sciences, Ahmedabad University, Ahmedabad, India
2
School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, USA
Received:
5
April
2025
Accepted:
3
June
2025
Published online:
23
June
2025
We present an enhancement to Grover’s search algorithm for instances where the number of items (or the size of the search problem) N is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, we demonstrate that a considerable reduction in the number of oracle calls (and Grover iterations) can be achieved in many cases. For special cases, the reduction in the number of oracle calls and Grover iterations asymptotically approaches 29.33%. This improvement is significant compared to the traditional Grover’s search algorithm, which handles such cases by rounding N up to the nearest power of 2. The key to this improvement is our algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, which has gate complexity and circuit depth of only 
, without using any ancilla qubits.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
