



01304nas a2200133   4500008004100000245010100041210006900142260001400211520085700225100001701082700001901099700001501118856003701133       2021                        eng d00aHyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations0 aHyperInvariant MERA Approximate Holographic Error Correction Cod  c3/15/20213 a<p>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.</p>1 aCao, ChunJun1 aPollack, Jason1 aWang, Yixu  uhttps://arxiv.org/abs/2103.08631