A four-level qubit system is applied to realize quantum half-adder operation. The half-adder circuit is obtained in terms of a quantum CPHASE gate realized by the qubits comprised of four energy levels [C. P. Yang, Prog. Theor. Phys. 128, 587 (2012)], and such a CPHASE gate is demonstrated using the transmon. Commonly, higher energy levels are very sensitive and are easily perturbed by the noise sources. Compared to other qubit systems, the higher energy levels of the transmon are less prone to noise such as charge noise, flux noise and other noises. Further, the order of the dephasing time of the higher energy levels (third and fourth energy levels) is nearly the same as that of the lower energy levels of the transmon when the ratio between the Josephson energy and the charging energy ≫ 1. A system of three transmons coupled to a single high quality-factor superconducting coplanar resonator is demonstrated to obtain two- and three-qubit CPHASE gates which are in turn used to obtain the quantum half-adder operation. The main advantage of this quantum half-adder scheme is the reduction in the number of required elementary gates, leading to a significant increase in operational speed and robustness compared to the other existing half-adder schemes. The operational time of a complete half-adder operation is ∼ 37 ns. The methods presented in this article can also be implemented for more complicated quantum circuits.