A qubit is an element of a two-dimensional Hilbert space and is the basic unit of quantum information. A quantum gate is a unitary operator on several qubits. A quantum circuit is a process of performing operations given by a combination of finite qubits and quantum gates. However, quantum computers are sensitive to external factors, so topological quantum error correction have emerged to prevent this. In this talk, I introduce a brief history of quantum computation and former results of topological quantum error correction. Furthermore I suggest the way for connecting Quantum Information Theory and Quantum Knot Theory.