# Efficient Design of Reversible Adder and Multiplier Using Peres Gates
## 1 Introduction  
The ever-evolving landscape of digital computing demands innovative solutions to address the challenges posed by emerging technologies. Reversible logic has gained prominence for its unique ability to perform computations in a manner that enables the retrieval of input states from output states [1]. The potential uses of reversible logic include low-power computing, where large-scale data centers and energy-efficient computing reduce overall power consumption, leading to greener and more sustainable data processing [2; 3]. In quantum computing, error-correcting codes and reversible logic help in creating fault-tolerant quantum circuits [4; 5]. Since no information is lost, reversible logic facilitates the complete and verifiable erasure of data, which is critical for privacy and security. Reversible logic also has applications in DNA-based computation [6] and molecular computing [7], useful in areas like drug discovery and bio-molecular sensing. The nano-electronics devices operate at less power, having nanotechnology applications [8]. Reversible logic circuits are being studied as an alternative to classical CMOS circuits, potentially leading to more compact and efficient chip design. Reversible logic plays an important role in creating more energy-efficient artificial intelligence accelerators and neural networks [9]. The adders, multipliers, and other arithmetic units constructed from reversible logic lead to improvements in digital signal processing and digital image processing [10]. Reversible logic has the potential to revolutionize the computing world by enabling more energy-efficient, sustainable, and scalable systems across a wide range of industries. Reversible logic is a field of study on developing circuits where the input is uniquely recovered from the outputs, which means there is no loss of information during computation [11]. Some of the state-of-the-art technologies and approaches in reversible logicinclude quantum technologies, adiabatic logic, CMOS-based reversible circuits, emerging reversible logic gates, fault-tolerant reversible computing, reversible logic synthesis, and neuro-morphic and beyond CMOS computing. The quantum gates are reversible by nature. The surface code uses reversible logic to minimize errors during quantum computations, as qubits are prone to errors from external noise [12]. Adiabatic logic circuits are increasingly used in applications requiring minimal power consumption, such as battery-operated devices, sensor networks, and wearables. Techniques like dual rail logic and pass transistor logic are employed to build reversible circuits that are compatible with existing CMOS technology. Reversible logic is being applied to nano-electronics to develop extremely small, low-power, high-performance computational devices. Technologies like quantum dot cellular automata (QCA) and single electron transistors (SETs) are being used to explore reversible logic at the nanoscale [13; 14]. Reversible circuits are also explored for fault tolerance in computing systems. These designs are less prone to errors compared to conventional irreversible logic circuits, which makes them attractive for mission-critical applications like space computing and medical devices. Research is being conducted into photonic circuits that use light instead of electricity to implement reversible logic. Optical reversible logic gates such as Mach-Zehnder interferometers perform computation with lower energy dissipation [15]. Reversible logic is also applied in quantum photonic computing, where photons are used as information carriers to implement efficient and fast reversible operations. Advanced software tools are being developed to automatically synthesize reversible circuits from high-level descriptions [16]. These tools focus on minimizing gate count and quantum cost, which are critical metrics in reversible computing. Ongoing research is directed at optimizing reversible circuits in terms of quantum cost, gate count, etc.