MATLAB Programming to Implement Quantum Walk Algorithm for Presenting Probability Distributions of Quantum Walks

Authors

  • Lila Yuwana Department of Physics, Institut Teknologi Sepuluh Nopember, Surabaya
  • Agus Purwanto Department of Physics, Institut Teknologi Sepuluh Nopember, Surabaya
  • Endarko Endarko Department of Physics, Institut Teknologi Sepuluh Nopember, Surabaya

DOI:

https://doi.org/10.26713/jims.v10i1-2.685

Keywords:

Quantum Walks, probability distributions, coin flip transformation

Abstract

There are numerous ideas that have been provided by quantum walks for new quantum algorithms. In this article, we surveyed the discrete quantum walk algorithm to present probability distributions. Moreover, we transformed the algorithm into MATLAB programming. Finally, the programming can be utilised to compare coin flip transformations that generate probability distributions as proposed in several previous articles and also to identify a unitarity of a coin flip transformation.

Downloads

Download data is not yet available.

References

Y. Aharonov, L. Davidovich and N. Zagury, Quantum random walks, Physical Review A 48 (1993), 1687 – 1690.

A. Ambainis, E. Bach, A. Nayak, A. Vishwanath and J. Watrous, One-dimensional quantum walks, in The Thirty-Third Annual ACM Symposium on Theory of Computing (STOC'01), New York (2001).

A. Ambainis, Quantum walks and their algorithmic applications, International Journal of Quantum Information 10 (4) (2003), 507.

N. Ashwin and V. Ashvin, Quantum Walk on the Line, Center for Discrete Mathematics & Theoretical Computer Science, New York (2000).

A.M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Guttman and D.A. Spielman, Exponential algorithmic speedup by quantum walk, in Proceedings 35th ACM Symposium on Theory of Computing (STOC 2003), San Diego (2003).

J. Kempe, Quantum random walks: An introductory overview, Contemporary Physics 44 (2003), 307 – 327.

M. Montero, Quantum and random walks as universal generators of probability distributions, Physical Review A 95 (2017), 062326; 062326-1.

R. Motwani and P. Raghavan, Randomized Algorithms, 1st edition, Cambridge University Press (1995), New York.

M.N. Dheeraj and A.T. Brun, Continuous limit of discrete quantum walks, Physical Review A 91 (6) (2015), 062304-1.

Downloads

Published

2018-04-30
CITATION

How to Cite

Yuwana, L., Purwanto, A., & Endarko, E. (2018). MATLAB Programming to Implement Quantum Walk Algorithm for Presenting Probability Distributions of Quantum Walks. Journal of Informatics and Mathematical Sciences, 10(1-2), 23–32. https://doi.org/10.26713/jims.v10i1-2.685

Issue

Vol. 10 No. 1-2 (2018)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.