时序量子机的积及其矩阵形式

Products of Sequential Quantum Machines and Their Matrix Forms

时序量子机(SQM)首先由Gudder提出,之后邱道文提出了时序量子机的等价模型即量子时序机(QSM),并解决了Gudder提出的公开问题。本文定义了时序量子机的如下直积:广义直积、全直积、限制直积、级联积、圈积、合成积、直和,并对每一种积的状态集的两种不同状态顺序,给出它们的矩阵形式。

Sequential quantum machine （SQM） was firstly proposed by Gudder. Qiu Daowen proposed quantum sequential machine （QSM） which is the equivalent model of sequential quantum machine later, and solved the open problem which was proposed by Gudder. In this paper, the following products of sequential quantum machines are defined： general direct product, full direct product, restricted direct product, cascade product, wreath product, composition product and direct sum. For each kind of product and for two different orders of the state set, their matrix forms are given.