Analysis and Implementation of Quantum Gates (X, Z, Y, Hadamard CNOT and CCNOT) by using matrices for Quantum Computing

The constraints of present supercomputers in addressing exponentially intricate problems are apparent, as these jobs sometimes necessitate hundreds or even thousands of years due to the exponential increase in computational requirements. Quantum computing, which utilizes concepts from quantum physics and operates with qubits, offers a promising solution by significantly decreasing problem-solving durations to only seconds or minutes. Using IBM's quantum computing platform, this work investigates the construction and analysis of fundamental quantum gates, including X, Z, Y, Hadamard, CNOT, and CCNOT. This work presents a comprehensive analysis of these gates using matrix representations, demonstrating their operational mechanics and algebraic functions, and fundamental role of matrix theory in quantum gate operations and its contribution to the future development of quantum computing.