With the emergence of quantum physics and computer science in the 20th century, a new era was born which can solve very difficult problems in a much faster rate or problems that classical computing just can't solve. In the 21st century, quantum computing needs to be used to solve tough problems in engineering, business, medical, and other fields that required results not today but yesterday. To make this dream come true, engineers in the semiconductor industry need to make the quantum circuits a reality. To realize quantum circuits and make them scalable, they need to be fault tolerant, therefore Clifford+T gates need to be implemented into those circuits. But the main issue is that in the Clifford+T gate set, T gates are expensive to implement. Carry Look-Ahead addition circuits have caught the interest of researchers because the number of gate layers encountered by a given qubit in the circuit (or the circuit's depth) is logarithmic in terms of the input size n. Therefore, this thesis focuses on optimizing previous designs of out-of-place and in-place Carry Look-Ahead Adders to decrease the T-count, sum of all T and T Hermitian transpose gates in a quantum circuit.