标题： 基于发射器的光子图态生成协议的优化复杂度和资源最小化 显示英文标题

标题： Optimization complexity and resource minimization of emitter-based photonic graph state generation protocols

摘要： 光子图态对于基于测量和融合的量子计算、量子网络和传感非常重要。原则上，可以通过使用发射器来创建所需的纠缠来确定性地生成它们。找到减少发射器之间纠缠门数量的方法，并理解此类协议的整体优化复杂性对于实际实现至关重要。在这里，我们使用图论概念来解决这些问题。我们开发了优化器，以最小化纠缠门的数量，与朴素方案相比，对于中等大小的随机图，减少了最多75$\%$。虽然优化发射器-发射器CNOT计数的复杂性可能是NP难的，但我们能够基于图变换和稳定子电路优化之间的强连接开发启发式方法。这些模式使我们能够处理大型图，并且在不依赖细微指标（如边密度）的情况下，仍能实现发射器CNOTs最多$66\%$的减少。我们找到了准备任何大小的未编码和编码中继图态的最佳发射顺序和电路，尽管两个优化问题的平均复杂性都是NP难的，但仍实现了发射器和CNOT资源的全局最小化。我们进一步研究了图的局部等价轨道。虽然对于任意图来说枚举轨道是$\#$P完全的，但我们分析计算了中继图轨道的大小，并找到了生成任何中继大小轨道的过程。最后，我们检查了从给定轨道准备任何图的纠缠门成本，并表明我们可以在整个轨道中实现相同的最优CNOT计数。 显示英文摘要

摘要： Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding ways to minimize the number of entangling gates between emitters and understanding the overall optimization complexity of such protocols is crucial for practical implementations. Here, we address these issues using graph theory concepts. We develop optimizers that minimize the number of entangling gates, reducing them by up to 75$\%$ compared to naive schemes for moderately sized random graphs. While the complexity of optimizing emitter-emitter CNOT counts is likely NP-hard, we are able to develop heuristics based on strong connections between graph transformations and the optimization of stabilizer circuits. These patterns allow us to process large graphs and still achieve a reduction of up to $66\%$ in emitter CNOTs, without relying on subtle metrics such as edge density. We find the optimal emission orderings and circuits to prepare unencoded and encoded repeater graph states of any size, achieving global minimization of emitter and CNOT resources despite the average NP-hardness of both optimization problems. We further study the locally equivalent orbit of graphs. Although enumerating orbits is $\#$P complete for arbitrary graphs, we analytically calculate the size of the orbit of repeater graphs and find a procedure to generate the orbit for any repeater size. Finally, we inspect the entangling gate cost of preparing any graph from a given orbit and show that we can achieve the same optimal CNOT count across the orbit.