N The Matrix Expressions Of Quantum Bit Lines

In recent years, quantum information and quantum computing has becomea focus for researchers, their research object is the information processing tasksthat can be completed with quantum mechanical system.In order to betterunderstand quantum algorithms and quantum protocols of quantum computing,they are usually represented in the form of quantum circuits. Quantumcircuits. is a combination of series quantum gates, and each quantum gateactually corresponds to a unitary matrix. The output state is generated after thequantum gate effect on the input state. So analysis and design of quantumcircuits and the corresponding unitary matrix is very important for this process.In this paper we analyzes the quantum circuit and its corresponding unitarymatrix, then to give an example, we analyze the matrix representation of thequantum counting and the quantum gate neural network.In this paper, we first introduces rudimentary knowledge of the universalquantum circuit, which include the definition and matrix of qubit state; thedefinition and matrix of the quantum gates; how to represent the controlled Uoperation with the single-qubit gates and controlled NOT gate. That is the Z-Y-Zdecomposition of controlled U gate.Then, we describes a quantum parallel computing principle, quantumcounting principle, quantum neural network, quantum gate circuit neuralnetwork mode.The main part of this paper,we analysis the matrix expression of unitaryoperation composed with N single qubit gates, using the ZYZ decomposition ofsingle-qubit gate, two-qubit controlled U operation. Then we analysis the matrixexpression of Quantum counting and quantum gate circuit neuralnetwork,which verify the reliability of the matrix expression.