We propose a new formulation of Quantum Turing Ma- chines, as an extension of those proposed by Bernstein and Vazirani. For this new class of Quantum Turing Machines, both finite and infinite computations are meaningful -an infinite computation does not correspond trivially to a divergent function. Moreover, we propose a natural observation protocol for the new QTMs, that does not modify the probability of the possible outcomes of the machines. Finally, we use QTMs to define a class of quantum computable functions - any such a function is a mapping from a general quantum state to a distribution of probability of natural numbers.

中文翻译：

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量子图灵机：计算和测量

我们提出了一种新的量子图灵机公式，作为 Bernstein 和 Vazirani 提出的公式的扩展。对于这一类新的量子图灵机，有限和无限计算都是有意义的——无限计算并不简单地对应于发散函数。此外，我们为新的 QTM 提出了一种自然观察协议，它不会修改机器可能结果的概率。最后，我们使用 QTM 来定义一类量子可计算函数——任何这样的函数都是从一般量子态到自然数概率分布的映射。