标题： 量子实验与图 II：量子干涉、计算与态生成 显示英文标题

标题： Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation

摘要： 我们提出了一种概念性的新方法，使用图论来描述最先进的光子量子实验。 在那里，量子态由完美匹配的相干叠加给出。 关键观察是，在图中引入复数权重自然会导致量子干涉。 这一新观点立即带来了许多有趣的结果，其中一些我们在此提出。 首先，我们发现了一种新的、在实验上完全未被探索的多光子干涉现象。 其次，我们发现计算此类实验的结果是#P难的，这意味着它是一个经典难以处理的问题，涉及矩阵函数永久式及其推广的Hafnian的计算。 第三，我们解释了最近的一个否定结果如何普遍适用于线性光学量子实验，从而揭示了当前光子技术下量子态生成的重要见解。 第四，我们展示了如何以图形方式描述诸如纠缠交换之类的量子协议。 量子实验与图论之间揭示的桥梁为一种广泛应用的技术提供了新的视角，并立即引发了诸多后续问题。 显示英文摘要

摘要： We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. The new viewpoint immediately leads to many interesting results, some of which we present here. Firstly, we identify a new and experimentally completely unexplored multiphoton interference phenomenon. Secondly, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Thirdly, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights to quantum state generation with current photonic technology. Fourthly, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and Graph Theory offers a novel perspective on a widely used technology, and immediately raises many follow-up questions.