Quantum Matrices Using Quantum Gates

Quantum mechanics explains the behavior of matter and its movement with energy in the scale of atoms and subatomic particles. In quantum circuits there are many gates such as Hadamard Gate, Pauli Gates, many more gates for half turns, quarter turns, eighth turns, sixteenth turns and so on, rest for spinning, parametrized etc. Linear operators in general and quantum mechanics can be represented in the form of vectors and in turn can be viewed as matrices format because linear operators are totally equivalent with the matrices view point. This paper discloses creation of various quantum matrices using Quantum bits. Square, Identity and Transposition of matrices are performed considering whole process in entanglement. Angle, phase, coordinates, magnitude, complex numbers and amplitude has been noted and documented in this paper for further research.

量子力学（Quantum Mechanics）阐释了原子与亚原子粒子尺度下，物质的行为、运动规律及其能量相互作用。在量子电路中存在诸多量子门，例如哈达玛门（Hadamard Gate）、泡利门（Pauli Gates），此外还有大量用于半旋转、四分之一旋转、八分之一旋转、十六分之一旋转等操作的量子门，以及用于自旋调控、参数化的各类量子门等。通常而言，线性算子（Linear Operators）与量子力学相关运算均可通过矢量形式表示，进而可被转化为矩阵格式，这是由于从矩阵视角出发，线性算子与矩阵完全等价。本文公开了利用量子比特（Quantum Bits）构建各类量子矩阵的方法。本文在纠缠态（Entanglement）全流程下完成了矩阵的平方、单位矩阵及转置操作。本文记录并整理了角度、相位、坐标、模长、复数以及概率幅（Amplitude）等相关参数，以供后续研究参考使用。