量子角动量的耦合：对模拟/离散和局部/全局计算模型的洞察
Coupling of quantum angular momenta: an insight into analogic/discrete and local/global models of computation
摘要：
在过去的几年里，有一个动荡的活动，旨在为量子计算引入新的概念方案。Marzuoli A and Rasetti M 2002，2005 a中提出的方法依赖于SU（2）角动量的（再）耦合理论，可以被视为对基于“量子位”和布尔门的通常量子电路模型的自旋变量的任意值的推广。计算状态属于由离散和连续参数标记的有限维希尔伯特空间，并且幺正门可以依赖于在有限值集以及连续（角）变量上的量子数。这样一个框架是一个理想的游乐场，讨论离散（数字）和模拟计算过程，以及它们之间的关系发生时，一个一致的半经典限制发生在离散量子门。当使用纯离散的幺正门时，模拟器自然地被建模为量子有限状态的家庭-机器，这些机器反过来代表拓扑量子计算模型的离散版本。我们认为，我们的模型体现了一种统一的计算范式的灵感来自自然，甚至更雄心勃勃的，一个通用的设置，适当编码的量子符号操作的组合，拓扑和代数问题可能会找到他们的“自然”的计算参考模型。
英文摘要：
In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2) angular momenta and can be viewed as a generalization to arbitrary values of the spin variables of the usual quantum-circuit model based on `qubits' and Boolean gates. Computational states belong to finite-dimensional Hilbert spaces labelled by both discrete and continuous parameters, and unitary gates may depend on quantum numbers ranging over finite sets of values as well as continuous (angular) variables. Such a framework is an ideal playground to discuss discrete (digital) and analogic computational processes, together with their relationships occuring when a consistent semiclassical limit takes place on discrete quantum gates. When working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum finite states--machines which in turn represent discrete versions of topological quantum computation models. We argue that our model embodies a sort of unifying paradigm for computing inspired by Nature and, even more ambitiously, a universal setting in which suitably encoded quantum symbolic manipulations of combinatorial, topological and algebraic problems might find their `natural' computational reference model.
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