用最少数量量子发射器生成光子图态
Generation of Photonic Graph States with minimal number of quantum emitters
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- Paderborn University（帕德博恩大学）
- Quandela SAS（Quandela公司）
- LTCI, Inria, Télécom Paris, Institut Polytechnique de Paris（巴黎理工学院电信学院国家信息与自动化研究所通信与图像实验室）
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中文总结 AI 辅助
本研究提出四种启发式多项式算法，通过优化发射顺序减少光子图态制备所需的量子发射器数量，在随机图上实现高达30%的减少，并与现有门优化方案结合进一步减少约20%的双量子比特门。
中文摘要 AI 辅助
图态是测量型和融合型量子计算、量子网络及传感的基本资源。原则上，在光子系统中确定性地制备它们是可能的，但找到高效的制备方案一直是一个长期存在的问题，最近才得到解决。此外，人们还开发了用于减少所需双量子比特门数量的启发式优化方案。然而，通过优化发射顺序来减少发射器数量的问题尚未得到解决，这是由于它的计算复杂性，因为它与图论中一个著名的NP难问题——线性秩宽计算——相关联。在这项工作中，我们专注于开发启发式多项式算法以减少所需的发射器数量。我们总共提出了四种不同的算法，在随机图上展示了高达30%的发射器减少。此外，我们提供了数值和统计证据表明，我们的优化方案与用于优化制备协议双量子比特门的现有算法相结合，可以进一步减少约20%的门数量。最后，我们针对各种有用的图态族（例如用于基于测量的量子算法的图、用于量子纠错的簇态和图码）检验了所开发的算法，以确定每种算法的性能。
英文摘要
Graph states are a fundamental resource for measurement and fusion-based quantum computing, quantum networks, and sensing. Preparing them in a photonic system deterministically is, in principle, possible, but finding efficient schemes to prepare them was a long-standing problem addressed recently. Additionally, heuristic optimization schemes for reducing the required number of two-qubit gates were developed. However, the problem of reducing the number of emitters by optimizing the emission ordering was not addressed, due to its computational complexity, as it is connected to a well-known NP-hard problem from graph theory, the linear rank width computation. In this work, we focus on developing heuristic polynomial algorithms to reduce the number of emitters required. In total, we propose four distinct algorithms, which demonstrate up to $30\%$ emitter reduction on random graphs. Furthermore, we provide numerical and statistical evidence that the combination of our optimization schemes with the preexisting algorithms for optimizing the two-qubit gates of the preparation protocol can further reduce them by around $20\%$. Finally, we examine the developed algorithms for various useful graph state families, such as graphs useful for measurement-based quantum algorithms, and cluster states and graph codes used for quantum error correction, to determine the performance of each algorithm.
