Optimization and experimental realization of the quantum permutation algorithm

İ. Yalçınkaya and Z. Gedik
Phys. Rev. A 96, 062339 – Published 29 December 2017

Abstract

The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n-qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n-qubit case that the algorithm can be simplified so that it requires only O(n) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

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  • Received 2 October 2017

DOI:https://doi.org/10.1103/PhysRevA.96.062339

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

İ. Yalçınkaya1,* and Z. Gedik2

  • 1Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1-Staré Město, Czech Republic
  • 2Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, İstanbul, Turkey

  • *iskender.yalcinkaya@fjfi.cvut.cz

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Vol. 96, Iss. 6 — December 2017

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