AbstractWe 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.