World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×
Our website is made possible by displaying certain online content using javascript.
In order to view the full content, please disable your ad blocker or whitelist our website www.worldscientific.com.

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

The Parallel Quantum Algorithm for the Class of Optimization

    For the given n numbers without any other prior information, how to obtain the minimum norm of them only by assigning their signs before them? Moreover, how to know one number is the multiplication of which ones in the given n numbers? In classical solutions, enumeration is the only way via trying one by one, whose complexity is about O(n2n1) and this is a NP problem. In this paper, the parallel quantum algorithm is proposed to solve the two questions shown in above. Through the quantum design of linear expressions of angles in parallel circuits, only O(n2) time’s quantum operations and about O(n2) times’ quantum measurements in the average will give the correct answer in the successful probability of 0.97 instead of the traditional O(2n) times. The example and theoretical analysis demonstrate the efficiency of the proposed method.

    References

    • 1. Lev Davidovič Landau, Jevgenij Michajlovič Lifšic, J. B. Sykes and J. S. Bell, Quantum Mechanics: Non-Relativistic Theory (World Book Publishing Press, 1999). Google Scholar
    • 2. M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, Mathematical Structures in Computer Science 17(6) (2007) 1115–1115. ISIGoogle Scholar
    • 3. C. H. Bennett, G. Brassard, C. Crepeau et al., Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70(13) (1993) 1895–1899. Crossref, ISIGoogle Scholar
    • 4. J. C. Boileau, K. Tamaki, J. Batuwantudawe et al., Unconditional security of a three state quantum key distribution protocol, Phys. Rev. Lett. 94(4) (2005) 040503. Crossref, ISIGoogle Scholar
    • 5. C. Piltz, T. Sriarunothai, S. S. Ivanov, S. Wölk and C. Wunderlich, Versatile microwave-driven trapped ion spin system for quantum information processing, Science Advances 2 (2016) e1600093. Crossref, ISIGoogle Scholar
    • 6. Guanlei Xu, Xiaogang Xu, Xun Wang and Xiaotong Wang, Order-encoded quantum image model and parallel histogram specification, Quantum Information Processing 18 (2019) 346. Crossref, ISIGoogle Scholar
    • 7. Hai-Sheng Li, Ping Fan, Hai-Ying Xia et al., Quantum implementation circuits of quantum signal representation and type conversion, IEEE Trans. Circuits Syst. I: Regul. Pap. 2018 (2018) 1–14. Google Scholar
    • 8. P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proceedings of the 35th Annual Symposium Foundations of Computer Science, ed. S. Goldwasser (IEEE Computer Society Press, 1994), pp. 124–134. CrossrefGoogle Scholar
    • 9. A. Ekert and R. Jozsa, Quantum computation and Shor’s factoring algorithm, Rev. Mod. Phys. 68(3) (1996) 733–753. Crossref, ISIGoogle Scholar
    • 10. L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79(23) (1997) 325–328. CrossrefGoogle Scholar
    • 11. C. Zalka, Grover’s quantum searching algorithm is optimal, Phys. Rev. A 60(4) (1999) 2746–2751. Crossref, ISIGoogle Scholar
    • 12. M. Boyer, G. Brassard, P. Hoyer et al., Tight bounds on quantum searching, Fortsch. Phys.: Prog. Phys. 46(4 & 5) (1998) 493–505. Crossref, ISIGoogle Scholar
    • 13. Joseph L. Pachuau and Anish Kumar Saha, Generic conversion method for various spatial domain filters in quantum image processing, Quantum Information Processing (preprinted). Google Scholar
    • 14. D. Bertsimas and J. Tsitsiklis, Introduction to Linear Optimization (Athena Scientific, MA, 1997). Google Scholar
    • 15. A. A. Mohamed and B. Venkatesh, Line-wise optimal power flow using successive linear optimization technique, IEEE Transactions on Power Systems PP(3) (2019) 1-1. Google Scholar
    • 16. O. Inarejos, R. Hoto and N. Maculan, An integer linear optimization model to the compartmentalized knapsack problem, International Transactions in Operational Research (2019). Crossref, ISIGoogle Scholar
    • 17. Adalat Jabrayilov and Petra Mutzel, New Integer Linear Programming Models for the Vertex Coloring Problem, LATIN 2018: Theoretical Informatics (2018). CrossrefGoogle Scholar