论文标题
从复杂性几何学到全息时空
From Complexity Geometry to Holographic Spacetime
论文作者
论文摘要
ADS/CFT对应关系中的一个重要猜想将全息时段与双量子场理论的量子计算复杂性有关。但是，对这种关系的定量理解仍然是一个悬而未决的问题。在这项工作中，我们介绍并研究了计算复杂度度量与其全息图之间的图。我们考虑根据二维形成共形场理论中的共形转换构建的量子电路，以及基于通过Fubini-study距离为量子门分配成本的复杂度度量。我们在三维抗DE保姆的空间中找到了一个新颖的几何对象，这是该距离双重的。这种二元性还提供了在信息理论中定义的反de保姆宇宙的全息几何形状和复杂性几何形状之间的更一般图，其中每个点表示状态之间的状态和距离是由fubini-study study量子测量的。我们将新发现的二元性应用于永恒的黑洞时空，并在我们的方法中讨论了复杂性线性生长的起源和换回效果。
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open question. In this work, we introduce and study a map between a computational complexity measure and its holographic counterpart from first principles. We consider quantum circuits built out of conformal transformations in two-dimensional conformal field theory and a complexity measure based on assigning a cost to quantum gates via the Fubini-Study distance. We find a novel geometric object in three-dimensional anti-de Sitter spacetimes that is dual to this distance. This duality also provides a more general map between holographic geometry of anti-de Sitter universes and complexity geometry as defined in information theory, in which each point represents a state and distances between states are measured by the Fubini-Study metric. We apply the newly found duality to the eternal black hole spacetime and discuss both the origin of linear growth of complexity and the switchback effect within our approach.
