Quantum Physics

    

Computational Complexity in Quantum Computing

Authors: Koji Nagata, Do Ngoc Diep, Tadao Nakamura

Our aim is of studying the efficiency of two typical arithmetic calculations {[T. Nakamura and K. Nagata, Int. J. Theor. Phys. {\bf 60}, 70 (2021)]} using the principle of quantum mechanics. We demonstrate some evaluations of three two-variable functions which are elements of a boolean algebra composed of the four-atom set utilizing the Bernstein--Vazirani algorithm. This is faster than a classical apparatus, which would require $2^{12}=4096$ evaluations. Finally, using the three two-variable functions evaluated here, we demonstrate two typical arithmetic calculations in the binary system. Hence, our calculations are faster than a classical apparatus, which would require $2^{12}=4096$ evaluations.

Comments: 7 pages

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[v1] 2021-11-03 10:05:04

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