Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations

Abstract

We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.

12 pages plus appendices, 19 figures

References in corpus (9)

• A class of quantum many-body states that can be efficiently simulated
• Holography from Conformal Field Theory
• Tensor renormalization group approach to 2D classical lattice models
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Entanglement spectrum in one-dimensional systems
• Entanglement renormalization and topological order
• Holographic tensor network models and quantum error correction: A topical review
• Consistency Conditions for an AdS/MERA Correspondence
• The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics

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• Absolutely maximally entangled pure states of multipartite quantum systems
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding