2-Bit Multiplication Quantum Circuit with Addition

Abstract

This paper presents a groundbreaking exploration into quantum computing's capacity to revolutionize computational arithmetic through the development of a 2-bit multiplication quantum circuit. Leveraging the unique properties of quantum mechanics, particularly the phenomena of superposition and entanglement, this study navigates beyond classical computing limits. It intricately designs and implements a quantum circuit capable of multiplying two binary numbers, demonstrating a significant advancement in quantum computational technology. Utilizing qubits, the quantum analogs of bits, the circuit fundamentally redefines the multiplication process, adhering to quantum mechanics principles rather than classical binary operations. Our approach emphasizes the intricate orchestration of quantum gates within the circuit, with a particular focus on Controlled NOT (CNOT) and Toffoli gates. These are crucial for the arithmetic logic underpinning our multiplication task, illustrating the nuanced application of quantum theory to practical computation. The circuit showcases a pragmatic application of quantum computing principles, contributing to the burgeoning field of quantum algorithms. It serves as a vital stepping stone toward realizing more complex quantum arithmetic operations and their broader applications. Implemented using IBM's Qiskit, a versatile quantum computing software development framework, the circuit's design and functionality were rigorously tested in simulated environments. The results validate the circuit's efficiency and accuracy, confirming the successful quantum multiplication of 2-bit numbers. This work not only enriches the existing quantum algorithm repository but also sets a precedent for future quantum computing endeavors, particularly in optimizing and scaling quantum arithmetic operations.