内在泛n维量子元胞自动机
Intrinsically universal n-dimensional quantum cellular automata
摘要：
量子元胞自动机的定义有几种非公理化的方法。分块QCA（Partitioned QCA）是这些非公理化定义中最规范的。在这项工作中，我们首先表明，任何QCA可以放入PQCA的形式。我们的构造调和了QCA的所有非公理化定义，表明它们都可以相互模拟，因此它们都等价于公理化定义。接下来，我们描述了一个简单的n维QCA能够模拟所有其他的，在初始配置和任何n维QCA的前向演化可以被编码在初始配置的内在普遍的QCA，和几个步骤的内在普遍的QCA，然后对应于一个步骤的模拟QCA。这两个结果是正式的定义广义n维内在模拟，即模拟的概念，它保留了拓扑结构的意义上，每个单元格的模拟QCA编码为一组相邻的细胞在通用QCA。我们认为，这一概念带来了计算机科学为基础的概念的模拟和普遍性的一步更接近理论物理。
英文摘要：
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we first show that any QCA can be put into the form of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one another, and hence that they are all equivalent to the axiomatic definition. Next, we describe a simple n-dimensional QCA capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA, and that several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. Both results are made formal by defining generalised n-dimensional intrinsic simulation, i.e. a notion of simulation which preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. We argue that this notion brings the computer science based concepts of simulation and universality one step closer to theoretical physics.
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