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arXiv · 1708.07900

Optimization and experimental realization of the quantum permutation algorithm

İ. Yalçınkaya·Z. Gedik
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Abstract

The quantum permutation algorithm provides computational speed-up over classical algorithms in 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. In order 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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İ. Yalçınkaya, Z. Gedik. 2017-12-29. Optimization and experimental realization of the quantum permutation algorithm. https://doi.org/10.1103/physreva.96.062339

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