Building holographic code from the boundary

TL;DR

This paper introduces a new method for constructing holographic quantum error-correcting codes by starting from boundary descriptions, enabling insights into bulk reconstruction and entanglement structures in holography.

Contribution

It presents a novel boundary-based approach to building holographic codes, diverging from traditional bulk tensor-network methods, and demonstrates emergent bulk structures from boundary entanglement.

Findings

Bulk qudits and encoding emerge from boundary entanglement patterns.

The approach reproduces key holographic properties like the Ryu-Takayanagi formula.

The method offers a new perspective on holographic code construction.

Abstract

Holographic quantum error-correcting code, the quantum-information structure hypothesized for the AdS/CFT correspondence, has being attracting increasing attention in new directions interrelating the studies of quantum gravity and quantum simulation. In this work, we initiate a novel approach for building holographic code that can be generally applied in potentially broad and interdisciplinary contexts. Our approach takes an "opposite" route to the conventional paradigm that is based on bulk tensor-networks. As illustrated in an exact model, we start from scalable descriptions of boundary qudits which can guide succinct quantum-circuit simulations, and rigorously show how the bulk qudits and the encoding structure emerge from boundary entanglement patterns. By investigating the entanglement patterns, we systematically unfold the hypothetical structure for bulk reconstruction and the details of the Ryu-Takayanagi formula in the formalism of operator-algebra quantum error correction, demonstrating desired properties that are not yet proved in the established models. Our work might offer a fresh perspective for the study of holographic code.