Mathematical digital quantum computation by means of much more logical skills

We expand Deutsch’s algorithm for determining the mappings of a logical function using four orthogonal states. Using this, we propose a parallel computation for all of the combinations of values in variables of a logical function 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 \((1+1)\) $(1+1)$ and \((2+3)\) $(2+3)$ . The typical arithmetic calculation \((2+3)\) $(2+3)$ is faster than that of its classical apparatus which would require \(4^3=64\) $4^3=64$ steps when we introduce the full adder operation. Another typical arithmetic calculation \((1+1)\) $(1+1)$ is faster than that of its classical apparatus which would require \(4^2=16\) $4^2=16$ steps when we introduce only the half adder operation.