量子元胞自动机模型
Models of Quantum Cellular Automata
摘要：
本文系统地介绍了量子元胞自动机（QCA），它是量子计算的一种数学形式。首先给出了研究QCA模型的一般数学框架。然后，我们提出了四个不同的QCA模型，并比较它们。我们讨论的一个模型是传统的QCA，类似于Shumacher和Werner，Watrous和Van Dam介绍的模型。我们还讨论了马戈卢斯QCA，也讨论了舒马赫和维尔纳。我们介绍了两个新的模型，有色QCA和连续时间QCA。我们还将我们的模型与已建立的模型进行了比较。我们给出了这些模型的计算等价性的证明。我们展示了每个模型的优势，并提供了我们的模型如何有助于提出算法的例子，并在现实世界的物理设备中实现它们。
英文摘要：
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different QCA models, and compare them. One model we discuss is the traditional QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam. We discuss also Margolus QCA, also discussed by Schumacher and Werner. We introduce two new models, Coloured QCA, and Continuous-Time QCA. We also compare our models with the established models. We give proofs of computational equivalence for several of these models. We show the strengths of each model, and provide examples of how our models can be useful to come up with algorithms, and implement them in real-world physical devices.
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