论文标题
来自外来时空R4的量子计算和测量
Quantum computation and measurements from an exotic space-time R4
论文作者
论文摘要
作者先前通过利用与关系的自由组$ g $的子组的固定结构，找到了通用量子计算的模型。 $ g $的有效亚组$ h $导致“魔术”状态$ \ weft |ψ\右\ rangle $ $ d $ d $ d $ d $二维的希尔伯特空间，该空间编码了最小信息完整的量子测量（或麦克风），可能具有有限的“上下文”的几何形式。在目前的工作中，我们选择$ g $作为基本组$π_1（v）$ 4 $ - manifold $ v $，更确切地说是一个“小奇异”（时空）$ r^4 $（这是同型和等值的，而不是euclidean $ \ nymorphic，但对euclidean $ \ nath $ \ mathbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb {r}由于S. akbulut和R.〜e，我们选择的例子。 GOMPF，具有两个引人注目的属性：（i）显示出标准上下文几何形状（例如Fano Plane（指数$ 7 $））的出现，Mermin的Pentagram（指数$ 10 $），两Q Qubit的换向率图片$ GQ $ GQ（2,2）$（2,2,2）$（in Index $ 15 $）以及Combinatorial $ $ $ $ $（$）$ 28 $（2,8）麦克风测量的解释是由这种异国情调（时空）$ r^4 $的解释。我们与拓扑量子计算和异国时空相关的新图片也旨在成为“量子重力”的一种方法。
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state $\left|ψ\right\rangle$ in $d$-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite 'contextual' geometry. In the present work, we choose $G$ as the fundamental group $π_1(V)$ of an exotic $4$-manifold $V$, more precisely a 'small exotic' (space-time) $R^4$ (that is homeomorphic and isometric, but not diffeomorphic to the Euclidean $\mathbb{R}^4$). Our selected example, due to to S. Akbulut and R.~E. Gompf, has two remarkable properties: (i) it shows the occurence of standard contextual geometries such as the Fano plane (at index $7$), Mermin's pentagram (at index $10$), the two-qubit commutation picture $GQ(2,2)$ (at index $15$) as well as the combinatorial Grassmannian Gr$(2,8)$ (at index $28$) , (ii) it allows the interpretation of MICs measurements as arising from such exotic (space-time) $R^4$'s. Our new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of 'quantum gravity'.
