Reversible logic has attracted significant attention recently due to its inherent ability to decrease energy dissipation, which is the primary need of low-power digital circuits. One of the newest areas of study is reversible logic, which has applications in several areas, including nanotechnology, DNA computing, quantum computing, fault tolerance, and low-power CMOS. On the other hand, Quantum-dot Cellular Automata (QCA) is one of the stunning approaches that can be used as an alternative to traditional technologies. An Arithmetic and Logic Unit (ALU) is considered for performing essential instructions such as addition, subtraction, division, multiplication, and logic operations, including OR, XOR, AND, and XNOR. In other words, ALUs perform essential functions in digital processing circuits because of their wide applications in Central Processing Units (CPUs). Accordingly, ALUs have become a necessary part of microprocessors and are extensively used to solve procedural problems more efficiently and reliably. Hence, this paper proposes an efficient ALU with low power and high speed. At first, a full adder and a 4:1 multiplexer circuit are developed using a unique reversible gate. At last, using all the suggested circuits, an ALU with four mathematical and logical operations is developed. Moreover, several physical validations are presented to confirm the functionality of the QCA gate. The simulations of the structures and power consumption analysis are performed using QCADesigner 2.0.03 and QCAPro software. The suggested ALU's consumption power under various energy ranges (0.5 Ek, 1 Ek, and 1.5 Ek) showed significant advancements from previous designs.