从量子元胞自动机到量子晶格气体
From quantum cellular automata to quantum lattice gases
摘要：
纳米级量子计算的一种自然结构是量子元胞自动机。基于这一观察，在本文中，我们开始调查的正是酉元胞自动机。在证明了一维不存在非平凡的、齐次的、局部的、酉的、标量的元胞自动机之后，我们削弱了齐次条件，证明了存在非平凡的、精确酉的、划分的元胞自动机。我们发现一个参数家庭的演化规则，最好的解释为一个粒子的量子自动机。这个模型自然地重新制定为一个两个组件的元胞自动机，我们证明限制狄拉克方程。我们描述了两个推广的自动机，其中第二个，多个相互作用的粒子，是正确的定义的量子格子气。
英文摘要：
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.
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