幺正矩阵

本文利用双曲Euler公式[1]，给出了双曲平面H上的一类乘闭子集S2与一类幺正矩阵群U2[2]同构，证明并具体刻划了H平面上的线性变换与Lorentz变换的关系。

A class of multiplicatively closed Subsets S_2 that is isomorphic to a class of unitary matrix groups U_2 is given by Hyperbolic Euler transformation in this paper . The relation of linear transformation to Lorentz transformation on Hyperbolic plane H is also illustrated in detail .

简述了量子计算机的并行算法。设计了一个2n+12n+1的幺正矩阵，并根据量子Grover搜索算法求解出在无序数据库中满足条件的单项或多项数据的计算方法。

The paper explains the algorithm of quantum computation , designs a 2 n + 1 2 n + 1 unitary matrix , and gives a quantum searching of one datum or many data in database according to Grover Quantum Search .

表象间的基矢变换与幺正矩阵关系的再讨论

Further Discussion on the Relation between Base Vector Transformation and Unitary Matrix among Representations

给出了实现通信的量子线路，并以该线路为基础计算了Bell基及对应的幺正变换矩阵和量子门。

The circuitry of quantum communication is provided , and the author obtains Bell radix and quantum gate for corresponding unitary transformation matrix by the circuitry .

Wei-Norman分解对于分析矩阵微分方程的解是比较成熟的理论，含有幺正演化矩阵的薛定谔方程是矩阵微分方程，所以可以利用Wei-Norman分解来分析求出多能级量子系统的解。

Wei-Norman decomposition is a well known theory for solving matrix differential equations . The Schrdinger Equation with unitary evolution equations is a matrix differential equations , so Wei-Norman decomposition can be used for solving the multi-level quantum systems .

还证明了两种固体分界面上弹性波的散射矩阵是幺正厄米矩阵。

In addition , it is proved that the seattering matrixes of elastic waves on solid-solid boundary surface are unitary Hermite ones .