Quantum Physics

    

Mathematical Digital Quantum Computation by Means of Much More Logical Skills

Authors: Koji Nagata, Tadao Nakamura

We expand Deutsch's algorithm for determining the mappings of a logical function by using four orthogonal states. Using this, we propose a parallel computation for all of the combinations of values in variables of a logical function by using sixteen orthogonal states.As an application of our algorithm, we demonstrate two typical arithmetic calculations in the binary system. We study an efficiency for operating a full adder/half adder by quantum-gated computing. The two typical arithmetic calculations are $(1+1)$ and $(2+3)$.The typical arithmetic calculation $(2+3)$is faster than that of its classical apparatus which would require $4^3=64$ steps when we introduce the full adder operation. Another typical arithmetic calculation $(1+1)$is faster than that of its classical apparatus which would require $4^2=16$ steps when we introduce only the half adder operation.

Comments: 14 Pages. Quantum Studies: Mathematics and Foundations, (Accepted 2024.02.09).

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Submission history

[v1] 2022-12-21 02:41:43
[v2] 2024-02-12 23:11:43

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