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arXiv 2009.09096quant-phcs.NAmath.NA
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光滑可微函数量子叠加的纠缠性质

Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions

Adam Holmes, A. Y. Matsuura

摘要:

我们提出了一个纠缠分析的量子叠加对应的光滑,可微,实值(SDR)单变量函数。SDR功能示出可缩放的近似低秩矩阵产品状态,大系统离散化。我们发现,这些功能的最大冯诺依曼二分熵的增长与系统的大小grammically。这意味着,有效的低秩近似这些功能存在于一个矩阵产品状态(MPS)的大型系统。作为一个推论,我们显示了一个上界的迹距离近似精度为秩2 MPS为$Ω(\log N/N)$,这意味着这些低秩近似可以准确地为大型量子系统的规模。

英文摘要:

We present an entanglement analysis of quantum superpositions corresponding to smooth, differentiable, real-valued (SDR) univariate functions. SDR functions are shown to be scalably approximated by low-rank matrix product states, for large system discretizations. We show that the maximum von-Neumann bipartite entropy of these functions grows logarithmically with the system size. This implies that efficient low-rank approximations to these functions exist in a matrix product state (MPS) for large systems. As a corollary, we show an upper bound on trace-distance approximation accuracy for a rank-2 MPS as $Ω(\log N/N)$, implying that these low-rank approximations can scale accurately for large quantum systems.

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