Using the framework of Tutte embeddings, we begin an exploration of \emph{quantum graph drawing}, which uses quantum computers to visualize graphs. The main contributions of this paper include formulating a model for quantum graph drawing, describing how to create a graph-drawing quantum circuit from a given graph, and showing how a Tutte embedding can be calculated as a quantum state in this circuit that can then be sampled to extract the embedding. To evaluate the complexity of our quantum Tutte embedding circuits, we compare them to theoretical bounds established in the classical computing setting derived from a well-known classical algorithm for solving the types of linear systems that arise from Tutte embeddings. We also present empirical results obtained from experimental quantum simulations.

翻译：基于图特嵌入框架，我们开始探索利用量子计算机可视化图形的"量子图绘制"领域。本文的主要贡献包括：构建量子图绘制模型、描述如何从给定图创建图绘制量子电路，以及展示如何将图特嵌入计算为该电路中的量子态，进而通过采样提取该嵌入。为评估量子图特嵌入电路的复杂度，我们将其与经典计算环境下基于经典算法（用于求解图特嵌入中产生的典型线性系统）确立的理论边界进行比较，并展示从量子仿真实验中获得的实证结果。