论文标题
经典与量子：比较LHC数据上的基于网络的量子电路
Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
论文作者
论文摘要
张量网络（TN）是高维张量的近似值，旨在有效地表示局部纠缠的量子多体系统。这项研究在高度复杂的，模拟的LHC数据上进行了机器学习的背景下，在经典TNS和TN启发的量子电路之间进行了全面比较。我们表明，经典的TNS需要指数型较大的键尺寸和更高的希尔伯特空间映射才能与量子相对的同行。尽管这种维度的这种扩展可以更好地性能，但我们观察到，随着维度的提高，经典TNS导致了高度平坦的损失景观，从而使基于梯度的优化方法的使用极具挑战性。此外，通过采用定量指标（例如Fisher信息和有效的维度），我们表明经典TNS需要更广泛的训练样本，以像TN启发的量子电路一样有效地表示数据。我们还参与了混合经典量子型TN的想法，并显示了可能从数据中使用较大相位空间的架构。我们使用三个主要TN ANSATZ提供结果：树张量网络，矩阵产品状态和多尺度纠缠重态化Ansatz。
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of Machine Learning on highly complex, simulated LHC data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase-space from the data. We offer our results using three main TN ansatz: Tree Tensor Networks, Matrix Product States, and Multi-scale Entanglement Renormalisation Ansatz.
