Journal of Modern Research Physics
Volume 9, Issue 2 (Autumn and Winter 2024 2025)
JMRPh 2025, 9(2): 15-25 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Karimkhani A, Ghale’e َ. Exploring Quantum Adiabatic Conditions in a Generalized Quantum Algorithm. JMRPh 2025; 9 (2) :15-25
URL: http://jmrph.khu.ac.ir/article-1-260-en.html
URL: http://jmrph.khu.ac.ir/article-1-260-en.html
Tafresh University
Abstract: (139 Views)
Quantum adiabatic computing provides a framework for simulating quantum algorithms grounded in established quantum mechanics theorems. The quantum adiabatic theorem defines the conditions for the adiabatic transformation of quantum systems, but verifying these conditions demands careful scrutiny. This study focuses on the generalized Deutsch algorithm within the realm of quantum adiabatic computing. The time-dependent Hamiltonian is analyzed by evaluating the system's input and output states. The input state is a two-particle quantum entangled state, while the four output states represent the system's computational results. The allowed energy levels of the computational system are derived as the eigenstates of the Hamiltonian. By plotting these energy levels, the differences between them are quantified. Standard runtime functions are employed to validate the computational system, and various scheduled time functions are used to examine the applicability of the quantum adiabatic theorem to the generalized Deutsch algorithm. Analysis of the energy gaps between excited states and the ground state confirms that the proposed Hamiltonian satisfies adiabatic conditions throughout the algorithm's execution.
Keywords: generalized Deutsch algorithm, Energy level, Quantum Computing, Quantum Adiabatic Computing.
Type of Study: Research |
Subject:
Special
Received: 2025/03/16 | Accepted: 2025/06/30 | Published: 2025/03/15 | ePublished: 2025/03/15
Received: 2025/03/16 | Accepted: 2025/06/30 | Published: 2025/03/15 | ePublished: 2025/03/15
References
1. R. Rennie, Oxford Dictionary of Physics, 7rd ed., Oxford University Press, Oxford 2015.
2. M. A. Nielsen and, I.L. Chuang, Quantum Computation and Quantum Information. Cambridge, University Press, Cambridge, 2000
3. J. A. Buchmann, Introduction to Quantum Algorithms, American Mathematical Society, 2024.
4. V. M. Kendon, K. Nemoto, W. J. Munro, Quantum Analogue Computing,
5. Phil. Trans. R. Soc. A , 368:3621-3632, 2010 . [DOI:10.1098/rsta.2010.0039] [PMID]
6. T. Kadowaki, Enhancing Quantum in Digital-Analog Quantum Computing, APL Quantum, 1, 026101, 2024. [DOI:10.1063/5.0179540]
7. D. Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer," Proc. R. Soc. Lond. A., vol. 400, no. 1818, pp. 97-117, 1985 [DOI:10.1098/rspa.1985.0070]
8. D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. Lond. A., vol. 439, no. 1907, pp. 553-558, 1992. [DOI:10.1098/rspa.1992.0167]
9. E. Bernstein and U. Vazirani, "Quantum complexity theory," in Proc. of the Twenty-Fifth Annual ACM Symp. on Theory of Computing, STOC'93, pp. 11-20, San Diego, CA, USA, 16-18 May 1993. [DOI:10.1145/167088.167097]
10. D. Coppersmith, An approximate Fourier transform useful in quantum factoring,IBM Reseach Report No. RC19642, 1994.
11. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing, 26(5):1484-1509, 2005. [DOI:10.1137/S0097539795293172]
12. L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Physical Review Letters, 79(2):325-328, 1997. [DOI:10.1103/PhysRevLett.79.325]
13. C. Durr and P. Høyer, A quantum algorithm for finding the minimum, arXiv:quant-ph/9607014, 1996.
14. D. Janzing and P. Wocjan, A simple promiseBQP-complete matrix problem, Theory of Computing, 3:61-79, 2007. [DOI:10.4086/toc.2007.v003a004]
15. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum Computation by Adiabatic Evolution, arXive: quant-ph/001106.
16. A. M. Child, E. Farhi, and J. Preskill, "Robustness of adiabatic quantum computation," Phys. Rev. A, vol. 65, no. 1, pp. 0123220-01232210, Jan. 2002. [DOI:10.1103/PhysRevA.65.012322]
17. S. Das, R. Kobes, and G. Kunstatter, "Adiabatic quantum computation and Deutsch's algorithm" Phys. Rev. A, vol. 65, no. 6, pp.0623100-0623107, Jun. 2002. [DOI:10.1103/PhysRevA.65.062310]
18. T. Albash and D. A. Lidar "Adiabatic quantum computation", Rev. Mod. Phys., vol. 90, no. 1, pp. 0150020-0150035, Jan./Mar. 2018. [DOI:10.1103/RevModPhys.90.015002]
19. K. Nagata and T. Nakamura, "Some theoritically organized algorithm for quantum computer" Int. J. Theor. Phys., vol. 59, no. 2, pp. 611-621, 2020. [DOI:10.1007/s10773-019-04354-7]
20. K. Nagata and T. Nakamura, "Generalization of Deutsch's algorithm" Int. J. Theor. Phys., vol. 59, no. 8, pp. 2557-2661, 2020 [DOI:10.1007/s10773-020-04522-0]
21. آرش کریم خانی و امیر قلعه, "بهینهسازی حالتهای اولیه برای رایانش کوانتومی آدیاباتیک در یک الگوریتم کوانتومی," مهندسی برق و مهندسی کامپیوتر ایران , جلد 21, شماره 4,
22. pp. 291-295, 1402.
23. J. Roland and N. J. Cerf, "Quantum search by local adiabatic evolution", Phys. Rev. A, vol. 65, p. 042308, 2002. [DOI:10.1103/PhysRevA.65.042308]
24. S. A. Adamson∗ and P. Wallden,'' Adiabatic quantum unstructured search in parallel'', ArXiv:2502.08594.
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |