基于动力学代数SU（1，1）的量子超计算
Quantum hypercomputation based on the dynamical algebra su(1,1)
摘要：
提出了一种Kieu超计算量子算法（KHQA）的改进算法。所使用的方法是用其他低维动力学代数来取代Weyl-Heisenberg代数，该代数允许具有自然定义的广义相干态的无限维不可约表示。我们选择了李代数$\mathfrak{su}(1,1)$，因为这种代数具有实现超计算的必要特征，也因为这种代数已被确定为与许多相对简单的量子系统相关联的动力学代数。除了KHQA在代数$\mathfrak{su}(1,1)$上的代数适应之外，我们还给出了KHQA在一些具体物理参考物上的适应：无限方势阱，无限圆柱势阱，扰动无限圆柱势阱，P{<$}sch-Teller势，Holstein-Primakoff系统和Laguerre振子。我们的结论是，它是可能的凝聚态物质和量子光学中有许多物理系统上，它是可能的，以考虑实施KHQA。
英文摘要：
An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl-Heisenberg algebra by other dynamical algebra of low dimension that admits infinite-dimensional irreducible representations with naturally defined generalized coherent states. We have selected the Lie algebra $\mathfrak{su}(1,1)$, due to that this algebra posses the necessary characteristics for to realize the hypercomputation and also due to that such algebra has been identified as the dynamical algebra associated to many relatively simple quantum systems. In addition to an algebraic adaptation of KHQA over the algebra $\mathfrak{su}(1,1)$, we presented an adaptations of KHQA over some concrete physical referents: the infinite square well, the infinite cylindrical well, the perturbed infinite cylindrical well, the P{ö}sch-Teller potentials, the Holstein-Primakoff system, and the Laguerre oscillator. We conclude that it is possible to have many physical systems within condensed matter and quantum optics on which it is possible to consider an implementation of KHQA.
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