什么时候量子元胞自动机（QCA）是量子格子气自动机（QLGA）？
When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?
摘要：
量子元胞自动机（QCA）是从量子模拟的角度特别感兴趣的量子计算模型。量子格子气自动机（QLGA - equivalently partitioned quantum元胞自动机）是QCA的一个有趣的子类. QLGA比QCA更深入地分析，而一般的QCA可能捕获更广泛的量子行为。因此，区分QLGA和QCA是一个重要的问题。尽管有很多先前的工作，分类QCA是QLGA仍然是一个悬而未决的问题。本文建立了无界有限量子元胞自动机（QCA）（在静止背景中有许多活动元胞）成为量子格子气自动机（QLGA）的充要条件。我们定义了一个局部条件，分类那些QCA是QLGA，我们表明，有QCA是不是QLGA。我们使用了一些工具，从功能分析的可分希尔伯特空间和表示理论的结合代数，使我们能够处理QCA有限，但无界配置的全部细节。
英文摘要：
Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. QLGA have been more deeply analyzed than QCA, whereas general QCA are likely to capture a wider range of quantum behavior. Discriminating between QLGA and QCA is therefore an important question. In spite of much prior work, classifying which QCA are QLGA has remained an open problem. In the present paper we establish necessary and sufficient conditions for unbounded, finite Quantum Cellular Automata (QCA) (finitely many active cells in a quiescent background) to be Quantum Lattice Gas Automata (QLGA). We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA. We use a number of tools from functional analysis of separable Hilbert spaces and representation theory of associative algebras that enable us to treat QCA on finite but unbounded configurations in full detail.
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