Adinkra图论中的量子比特
Qubits from Adinkra Graph Theory via Colored Toric Geometry
摘要：
我们开发了一种新的方法来处理量子比特信息系统，使用复曲面几何及其与Adinkra图论的关系。更准确地说，我们联系三个不同的主题，即环面几何，阿丁克拉斯和量子信息理论。这种一对一的对应关系可以被探索以使用被认为是理解包括弦论在内的现代物理学的有力工具的几何学来攻击量子比特系统问题。具体地说，我们对一个、两个和三个量子比特的情况进行了详细的研究，发现它们分别与\bf CP^1、\bf CP^1 \times CP^1和\bf CP^1 \times CP^1 \times CP^1环面变体相关联。使用被称为彩色复曲面几何的几何过程中，我们表明，量子位物理可以转换成一个场景处理复曲面数据的这种流形的帮助下，Adinkra图理论。对复曲面信息的操作可以产生通用的量子门。
英文摘要：
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory. This one to one correspondence may be explored to attack qubit system problems using geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with \bf CP^1, \bf CP^1\times CP^1 and \bf CP^1\times CP^1\times CP^1 toric varieties respectively. Using a geometric procedure referred to as colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of Adinkra graph theory. Operations on toric information can produce universal quantum gates.
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