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量子图灵机计算机(QTM)又称为通用量子计算机是一种用来模拟量子计算机效果的抽象机器。它提供了一个简单的模型，但又能展现出量子计算的所有威力。也就是说，任何量子算法都可以被形式化地表示为一个特定的量子图灵机。提供等效计算能力的量子电路是一种比较常用的模型。<ref name="equivalence" /><ref name="newequivalence" />

量子图灵机计算机(QTM)又称为通用量子计算机是一种用来模拟量子计算机效果的抽象机器。虽然它是一个简单的模型，但它能展现出量子计算的所有威力，因为任何量子算法都可以被形式化地表示为一个特定的量子图灵机。尽管说提供等效计算能力的量子电路是一种更常用的模型。<ref name="equivalence" /><ref name="newequivalence" />

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Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow.

Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow.

通过转移矩阵，量子图灵机可以与经典图灵机和概率图灵机相关联。兰斯 · 福特诺（Lance Fortnow）证明，指定一个矩阵，其与经典或概率图灵机的矩阵的乘积提供了量子机器的量子概率矩阵。<ref name="transition" />

通过过渡矩阵，量子图灵机可以与经典图灵机和概率图灵机相关联。兰斯 · 福特诺（Lance Fortnow）证明，量子图灵机的量子概率矩阵可以被拆解成是指定矩阵与经典或概率图灵机的矩阵的乘积。<ref name="transition" />

=== 通俗定义 ===

=== 通俗定义 ===

A way of understanding the quantum Turing machine (QTM) is that it generalizes the classical [[Turing machine]] (TM) in the same way that the [[quantum finite automaton]] (QFA) generalizes the [[deterministic finite automaton]] (DFA).  In essence, the internal states of a classical TM are replaced by [[pure state|pure]] or [[mixed quantum state|mixed states]] in a Hilbert space; the transition function is replaced by a collection of [[unitary matrix|unitary matrices]] that map the Hilbert space to itself.<ref name="Deutsch1985" />

A way of understanding the quantum Turing machine (QTM) is that it generalizes the classical [[Turing machine]] (TM) in the same way that the [[quantum finite automaton]] (QFA) generalizes the [[deterministic finite automaton]] (DFA).  In essence, the internal states of a classical TM are replaced by [[pure state|pure]] or [[mixed quantum state|mixed states]] in a Hilbert space; the transition function is replaced by a collection of [[unitary matrix|unitary matrices]] that map the Hilbert space to itself.<ref name="Deutsch1985" />

理解量子图灵机的一个方法是它推广了经典的图灵机，就像量子有限自动机推广了确定有限状态自动机机一样。实质上，经典 TM 的内部状态被希尔伯特空间中的纯态或混合态所取代，转移函数被映射 Hilbert 空间到自身的一组酉矩阵所取代。首次描述了图灵机的量子力学模型。牛津大学物理学家大卫 · 多伊奇在1985年的一篇文章中进一步发展了量子计算机的概念，他提出量子门可以以类似于传统数字计算二进制逻辑门的方式运行。

我们可以通过类比确定有限自动机（[[deterministic finite automaton]]）到量子有限自动机（[[quantum finite automaton]]）的转化来理解经典图灵机到量子图灵机的转化。 他们的差异在于，经典图灵机讨论的状态被推广到了希尔伯特空间（Hilbert space）中。希尔伯特空间是'''完备的内积空间'''，是有限维欧几里得空间的一个推广。它不局限于实数的情形和有限的维数，但又不失完备性。转换函数被一组映射 Hilbert 空间到自身的酉矩阵取代。<ref name="Deutsch1985" />

That is, a classical Turing machine is described by  a 7-[[tuple]] <math>M = \langle Q, \Gamma, b, \Sigma, \delta, q_0, F \rangle</math>.

That is, a classical Turing machine is described by  a 7-[[tuple]] <math>M = \langle Q, \Gamma, b, \Sigma, \delta, q_0, F \rangle</math>.

Iriyama, Ohya, and Volovich have developed a model of a linear quantum Turing machine (LQTM).  This is a generalization of a classical QTM that has mixed states and that allows irreversible transition functions.  These allow the representation of quantum measurements without classical outcomes.

Iriyama, Ohya, and Volovich have developed a model of a linear quantum Turing machine (LQTM).  This is a generalization of a classical QTM that has mixed states and that allows irreversible transition functions.  These allow the representation of quantum measurements without classical outcomes.