Efficient Implementation of a Quantum Search Algorithm for Arbitrary N

• URL: http://arxiv.org/abs/2406.13785v1
• Date: Wed, 19 Jun 2024 19:16:40 GMT
• Title: Efficient Implementation of a Quantum Search Algorithm for Arbitrary N
• Authors: Alok Shukla, Prakash Vedula,
• Abstract summary: This paper presents an enhancement to Grover's search algorithm for instances where $N$ 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's iterations) can be achieved in many cases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents 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's iterations) can be achieved in many cases. For special cases (i.e., when $N$ is of the form such that it is slightly greater than an integer power of 2), the reduction in the number of oracle calls (and Grover's iterations) asymptotically approaches 29.33\%. This improvement is significant compared to the traditional Grover's 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 requires gate complexity and circuit depth of only $ O (\log_2 (N)) $, without using any ancilla qubits.

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