量子图灵机的确定性停机
On Quantum Turing Machine Halting Deterministically
摘要：
我们定义了量子图灵机的一个子类SR-QTM，它具有确定性停机和确定性磁头位置。提出了描述SR-QTM的量子态跃迁图。借助于QSTD，我们构造了一个对所有近平凡变换都是普适的SR-QTM。这意味着存在对上述子类通用的QTM。最后，我们证明了SR-QTM与普通QTM在有界误差下是计算等价的。可以看出，由于SR-QTM对于不同的计算分支具有相同的时间步长，因此当将SR-QTM视为量子计算的模型时，将不存在停机方案问题。
英文摘要：
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we construct a SR-QTM which is universal for all near-trivial transformations. This means there exists a QTM which is universal for the above subclass. Finally we prove that SR-QTM is computational equivalent with ordinary QTM in the bounded error setting. It can be seen that, because SR-QTM has the same time steps for different branches of computation, the halting scheme problem will not exist when considering SR-QTM as a model of quantum computing.
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