Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and provide an approximation theory that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction.

中文翻译：

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来自小波理论的玻色子纠缠重整化电路

纠缠重整化是一种幺正实空间重整化方案。相应的量子电路或张量网络被称为 MERA，它们特别适合描述处于临界状态的量子系统。在这项工作中，我们展示了如何构建高斯玻色子量子电路，以实现任意自由玻色子链基态的纠缠重整化。该构造基于小波理论，将哈密顿量的色散关系转化为滤波器设计问题。我们给出了一个近似解决这个设计问题的通用算法，并提供了一个近似理论，该理论将滤波器的特性与相应量子电路的精度联系起来。最后，