A Review on Mathematical Approaches to Quantum Circuit Synthesis

Quantum computing is a new method of information processing based on the concepts of quantum mechanics which leads to strange and powerful events in the field of quantum. Each unitary matrix represents a quantum gate. Synthesis of quantum circuits refers to the process of converting a quantum gate into a series of basic gates implementable in quantum technologies and is divided into two general categories, namely decomposition and composition-based. In the first category, quantum circuits are synthesized by using matrix decomposition methods and in the second category, they are synthesized by using matrix multiplication of gates. This study deals with the first category, which uses mathematical algorithms to achieve the final characteristic of a quantum circuit.