Quantum Algorithms for optimizing problems

Diwakar Mainali; Megan Nagarkoti; Bijen Shrestha; Deepika Puri; Pranish Bista; Ojaswi Adhikari; Aanchal Nagarkoti Shrestha; Dr. Om Prakash sharma1

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Publication Date: 2024/08/14

Abstract: Quantum computing is quickly becoming a field that can change the game. It can completely change how businesses solve optimisation problems. We will be looking at three different quantum algorithms in great detail: the Quantum Approximate Optimisation Algorithm (QAOA), the Variational Quantum Eigensolver (VQE), and Grover's Algorithm. We look into how these algorithms work on the inside, how they compare to more traditional methods, and how they might be used in areas like energy, banking, and logistics. The piece then talks about current research projects that are trying to fix the technical issues and hardware limits of quantum technology. In the end, we look ahead to possible future developments that might help solve optimisation problems, such as better quantum gear and more complex quantum algorithms. By combining what has already been written with what is new, this study aims to shed light on how quantum computing could help solve tough optimisation problems and spark new ideas.

Keywords: Quantum Computing, Optimization Algorithms, Grover's Algorithm, Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), Quantum Hardware, Quantum Algorithms, Combinatorial Optimization, Quantum Error Correction, Future Directions.

DOI: https://doi.org/10.38124/ijisrt/IJISRT24AUG483

PDF: https://ijirst.demo4.arinfotech.co/assets/upload/files/IJISRT24AUG483.pdf

REFERENCES

  1. M. Cerezo et al., "Variational quantum algorithms," Nature Reviews Physics, vol. 3, no. 9, pp. 625-644, 2021.
  2. P. Ronagh, "Quantum algorithms for solving dynamic programming problems," arXiv preprint arXiv:1906. 02229, 2019.
  3. K. Bharti et al., "Noisy intermediate-scale quantum algorithms," Reviews of Modern Physics, vol. 94, no. 1, p. 015004, 2022.
  4. L. Bittel and M. Kliesch, "Training variational quantum algorithms is NP-hard," Physical Review Letters, vol. 127, no. 12, p. 120502, 2021.
  5. A. Gilyén, S. Arunachalam, and N. Wiebe, "Optimizing quantum optimization algorithms via faster quantum gradient computation," in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 2019, pp. 1425-1444.
  6. I. Kerenidis, A. Prakash, and D. Szilágyi, "Quantum algorithms for portfolio optimization," in Proceedings of the 1st ACM Conference on Advances in Financial Technologies, 2019, pp. 147-155.
  7. G. Verdon, J. M. Arrazola, K. Brádler, and N. Killoran, "A quantum approximate optimization algorithm for continuous problems," arXiv preprint arXiv:1902.00409, 2019.
  8. Y. H. Oh et al., "Solving multi-coloring combinatorial optimization problems using hybrid quantum algorithms," arXiv preprint arXiv:1911. 00595, 2019.
  9. D. Amaro et al., "Filtering variational quantum algorithms for combinatorial optimization," Quantum Science and Technology, vol. 7, no. 1, p. 015021, 2022.
  10. Z. C. Yang et al., "Optimizing variational quantum algorithms using pontryagin’s minimum principle," Physical Review X, vol. 7, no. 2, p. 021027, 2017.
  11. M. Lubasch et al., "Variational quantum algorithms for nonlinear problems," Physical Review A, vol. 101, no. 1, p. 010301, 2020.
  12. G. De Palma, M. Marvian, C. Rouzé, and D. S. França, "Limitations of variational quantum algorithms: a quantum optimal transport approach," PRX Quantum, vol. 4, no. 1, p. 010309, 2023.
  13. D. Pastorello, E. Blanzieri, and V. Cavecchia, "Learning adiabatic quantum algorithms over optimization problems," Quantum Machine Intelligence, vol. 3, pp. 1-19, 2021.
  14. D. Stilck França and R. Garcia-Patron, "Limitations of optimization algorithms on noisy quantum devices," Nature Physics, vol. 17, no. 11, pp. 1221-1227, 2021.
  15. C. Grange, M. Poss, and E. Bourreau, "An introduction to variational quantum algorithms for combinatorial optimization problems," 4OR, vol. 21, no. 3, pp. 363-403, 2023.