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Quantum-dot Cellular Automata (QCA) is novel prominent nanotechnology. It promises a substitution to Complementary Metal–Oxide–Semiconductor (CMOS) technology with a higher scale integration, smaller size, faster speed, higher switching frequency, and lower power consumption. It also causes digital circuits to be schematized with incredible velocity and density. The full adder, compressor, and multiplier circuits are the basic units in the QCA technology. Compressors are an important class of arithmetic circuits, and researchers can use quantum compressors in the structure of complex systems. In this paper, first, a novel three-input multi-layer full-adder in QCA technology is designed, and based on it, a new multi-layer 4:2 compressor is presented. The proposed QCA-based full-adder and compressor uses an XOR gate. The proposed design offers good performance regarding the delay, area size, and cell number comparing to the existing ones. Also, in this gate, the output signal is not enclosed, and we can use it easily. The accuracy of the suggested circuits has been assessed with the utilization of QCADesigner 2.0.3. The results show that the proposed 4:2 compressor architecture utilizes 75 cell and 1.25 clock phases, which are efficient than other designs. [ABSTRACT FROM AUTHOR]