14 March 2024, 13:15 (EET), Hall 300, INRNE

• Dr. Hristo Tonchev (INRNE-BAS)
• Title: Grover’s search algorithm with Multiphase matching
• Abstract: Grover's algorithm is a quantum algorithm for searching for elements that meet certain criteria in a linear unordered database. This algorithm, which was first introduced by Lov Grover [1] in 1996, requires one quantum register of size equal to the number of searched elements and is quadratically faster than the best classical search algorithms. Here we briefly review the Grover’s algorithm that uses qudits [2]. Next, we show the modification that uses Generalized Householder reflection. We investigate the robustness (stability against inaccuracies in the phases) of those modification. Generalized Householder can be used to construct two phase matching variants of the modification in order to make the Grover’s algorithm deterministic [3] [4]. However, achieving high probability requires maintaining a certain functional dependency between the phases. If multiple phases are used, the algorithm remains deterministic [5]. In addition, the robustness increases [6] and it is not required to maintain such a strict functional dependence between the phases used in both reflections of the algorithm’s iteration.
• References

  [1]

  L. K. Grover, Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, in STOC ’96.

  [2]

  S. S. Ivanov, H. S. Tonchev, and N. V. Vitanov, Phys. Rev. A, vol. 85, no. 6.

  [3]

  G. L. Long, Y. S. Li, W. L. Zhang, and L. Niu, Physics Letters A, vol. 262, no. 1.

  [4]

  P. Li and S. Li, Physics Letters A, vol. 366, no. 1.

  [5]

  F. M. Toyama, W. van Dijk, Y. Nogami, M. Tabuchi, and Y. Kimura, Phys. Rev. A, vol. 77, no. 4.

  [6]

  H. Tonchev and P. Danev, arXiv, Jan. 07, 2024.