Abstract: Loop is a very important program construct in classical computation. So, it is necessary to study the structure of the quantum Loop programs. This paper defines a general quantum Loop program whose body is a quantum operation, and gives the definitions for termination, almost termination and non-termination of the general quantum Loop program with respect to any input state. It proves the necessary and sufficient conditions for termination of the general quantum Loop programs given input state. As applications, it finally verifies the embedded quantum Loop programs whose body is unitary operation is a general quantum Loop program.

Key words: quantum computation, quantum Loop programs, quantum operation

摘要： 在经典计算中，Loop程序是非常重要的程序。对量子计算中Loop程序进行研究非常必要。定义了体为量子运算的广义量子Loop程序，给出了量子Loop程序在输入态上终止，几乎终止以及不终止的定义基于任意的初始态。并证明了量子Loop程序在给定输入态上终止的充要条件以及程序终止的充要条件。作为应用，验证了体为酉运算的量子Loop程序嵌套是一个广义的量子Loop程序。

关键词: 量子计算, 量子Loop程序, 量子运算