Implementation of 5-Qubit Quantum Search Algorithm with Analysis of Complexity and Scalability

doi:10.23940/ijpe.25.12.p4.705713

Abstract

Abstract: This publication shows the use of the quantum search algorithm by Grover to search unstructured data with a 5-qubit model in Qiskit. It is quadratically more likely to detect the correct state than in classical methods; the algorithm is more efficient in search. Simulated implementation demonstrates practically perfect amplification of the target state, whereas real IBM quantum hardware reveals the reality of practical issues of noise and gate errors. The results strengthen the possibility of quantum search methods on large unstructured data, and the possibility to reduce errors and scale protocols to better circuit designs.

Key words: quantum computing, Grover’s algorithm, unstructured data retrieval, Qiskit, quantum search, NISQ devices

Ashish Bhatt, Sumit Chaudhary, and Rashmi Kuksal. Implementation of 5-Qubit Quantum Search Algorithm with Analysis of Complexity and Scalability [J]. Int J Performability Eng, 2025, 21(12): 705-713.

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References

[1] Rieffel E., and Polak W., 2000. An introduction to quantum computing for non-physicists. ACM Computing Surveys (CSUR),32(3), pp. 300-335.
[2] Nagy M., and Akl S.G., 2006. Quantum computation and quantum information. the International Journal of Parallel, Emergent and Distributed Systems,21(1), pp. 1-59.
[3] Benioff P.,1980. The computer as a physical system: A microscopic quantum mechanical hamiltonian model of computers as represented by turing machines. Journal of Statistical Physics,22(5), pp. 563-591.
[4] Ladd T.D., Jelezko F., Laflamme R., Nakamura Y., Monroe C., and O’Brien J.L., 2010. Quantum computers. Nature,464(7285), pp. 45-53.
[5] Eisert J., and Wolf M.M., 2006. Quantum computing. InHandbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies, pp. 253-286.
[6] Nielsen M.A., and Chuang I.L., 2010. Quantum Computation and Quantum Information. Cambridge university press.
[7] Grover L.K.,1996. A fast quantum mechanical algorithm for database search. InProceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212-219.
[8] Raj G., Singh D., and Madaan A., 2017. Analysis of classical and quantum computing based on grover and shor algorithm. InSmart Computing and Informatics: Proceedings of the First International Conference on SCI 2016, Volume 2, pp. 413-423.
[9] Long G.L.,2001. Grover algorithm with zero theoretical failure rate.Physical Review A, 64(2), 022307.
[10] Toyama F.M., Van Dijk W., and Nogami Y., 2013. Quantum search with certainty based on modified grover algorithms: optimum choice of parameters. Quantum Information Processing,12(5), pp. 1897-1914.
[11] Garcia-Escartin J.C., and Chamorro-Posada P., 2011. Equivalent quantum circuits.Arxiv Preprint Arxiv:1110.2998.
[12] Mandviwalla A., Ohshiro K., and Ji B., 2018. Implementing grover’s algorithm on the IBM quantum computers. In2018 IEEE International Conference on Big Data (Big Data), pp. 2531-2537.
[13] Adedoyin A., Ambrosiano J., Anisimov P., Casper W., Chennupati G., Coffrin C., Djidjev H., Gunter D., Karra S., Lemons N., and Lin S., 2018. Quantum algorithm implementations for beginners.Arxiv Preprint Arxiv:1804.03719.
[14] IBM Quantum Platform, https://quantum.cloud.ibm.com/computers, accessed on December 1, 2025.
[15] IBM Inc., Introduction to Qiskit and IBM Quantum, https://qiskit.org/aqua, accessed on December 1, 2025.
[16] Saini S., Khosla P.K., Kaur M., and Singh G., 2020. Quantum driven machine learning. International Journal of Theoretical Physics,59(12), pp. 4013-4024.
[17] Brassard G., Hoyer P., Mosca M., and Tapp A., 2000. Quantum amplitude amplification and estimation.Arxiv Preprint Quant-Ph/0005055.
[18] Gilliam A., Pistoia M., and Gonciulea C., 2020. Optimizing quantum search using a generalized version of grover's algorithm.Arxiv Preprint Arxiv:2005.06468.