未初始化时序量子机的代数性质

Algebraic Properties of Uninitialized Sequential Quantum Machines

量子计算以其独有的内在可并行性和物理可实现性引起了人们的广泛关注.量子计算模型是量子计算领域最重要的问题之一.时序量子机和量子时序机是重要的量子计算模型,这两种计算模型本质上是等价的.本文利用代数的方法研究未初始化时序量子机的性质,这些性质为研究时序量子机提供了理论基础.首先,我们给出未初始化时序量子机同态的定义,得到了一些同态性质,并证明了同态定理;其次,我们研究未初始化时序量子机输入输出对的集合上的同余性质,以及未初始化时序量子机矩阵代数的性质,给出了可交换未初始化时序量子机的定义,并对可交换未初始化时序量子机的性质进行了讨论;最后,我们探讨未初始化时序量子机的等价性,讨论了一个可交换未初始化时序量子机的两个初始向量的等价性,所得结果改进了已有的一些结论.

Quantum computing has attracted extensive attention due to its intrinsic parallel computation and physical realization. Quantum computing model is one of the most impor- tant problems in the field of quantum computing. Sequential quantum machine and quantum sequential machine are two important quantum computing models, and they are essentially equivalent. In this paper, we study the properties of uninitialized sequential quantum machine by utilizing algebraic methods, which provide a theoretical basis for the study of sequential quantum machine. Firstly, we introduce the definition of homomorphism of uninitialized sequ- ential quantum machines. Some homomorphic properties of uninitialized sequential quantum machines are obtained, and the homomorphism theorem of uninitialized sequential quantum machines is proved. Secondly, we study the congruence properties on the set of input-output pairs of uninitialized sequential quantum machine and the matrix algebra properties of uninitialized sequential quantum machines. Moreover, a commutative uninitialized sequential quantum machine is defined, and its properties are discussed. Finally, the equivalence of uninitialized sequential quantum machines is established, and the equivalence of two initial vectors of a com- mutative uninitialized sequential quantum machine is discussed. The obtained results improve some existing results.