Bosonic entanglement renormalization circuits from wavelet theory

Abstract

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.

22 pages, 7 figures

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Cited by in corpus (4)

• Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets
• Entanglement in quantum field theory via wavelet representations
• Variational quantum simulation of critical Ising model with symmetry averaging
• Operator-algebraic renormalization and wavelets