随机高斯增强矩阵乘积态
Random Gaussian Augmented Matrix Product States
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中文总结 AI 辅助
本研究提出随机高斯增强矩阵乘积态（GAMPS），通过高斯酉变换增强张量网络，在适中键维下实现近最大体积律纠缠，并展现出态二设计行为，显著扩展了张量网络的表达能力。
中文摘要 AI 辅助
强纠缠限制了张量网络对量子多体系统描述的适用范围。我们研究了高斯增强矩阵乘积态（GAMPS），它通过将自由费米子（高斯）酉变换应用于矩阵乘积态而形成。为了探索这一族的能力，我们考虑了随机GAMPS，这是一种通过独立采样随机矩阵乘积态和高斯酉变换而获得的最小结构化系综。利用高斯酉变换的代数结构，我们开发了一种副本张量网络方法，可计算数百个量子比特的随机GAMPS系综上的平均值。随机GAMPS在适中的键维下就已展现出近乎最大的体积律纠缠，而其他量子资源度量则随着键维的增加迅速接近哈达玛随机态的值。纠缠标度表明，与未增强的矩阵乘积态相比，达到体积律熵所需的键维呈指数级减少。我们发现，在固定精度下，随机GAMPS表现出态二设计行为，且其键维与系统大小无关。我们的结果揭示了高斯增强如何扩展张量网络的表达能力。
英文摘要
Strong entanglement limits the reach of tensor-network descriptions of quantum many-body systems. We study Gaussian-augmented matrix product states (GAMPS), formed by applying a free-fermionic (Gaussian) unitary to a matrix product state. To explore the capabilities of this family, we consider random GAMPS}, a minimally structured ensemble obtained by independently sampling random matrix product states and Gaussian unitaries. Exploiting the algebraic structure of Gaussian unitaries, we develop a replica tensor-network method that computes averages over the random GAMPS ensemble for hundreds of qubits. Random GAMPS exhibit nearly maximal volume-law entanglement already at modest bond dimension, while other quantum resource quantifiers rapidly approach Haar-random state values as the bond dimension increases. The entanglement scaling suggests an exponential reduction in the bond dimension needed to approach the volume-law entropy compared with unaugmented matrix product states. We find a state two-design behavior of random GAMPS at fixed accuracy with a bond dimension independent of system size. Our results reveal how Gaussian augmentation expands the expressive power of tensor networks.
发表机构
- Barcelona Supercomputing Center（巴塞罗那超级计算中心）
- Technical University of Munich（慕尼黑工业大学）
- Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
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