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.
Universität Innsbruck（因斯布鲁克大学）；University of Gdańsk（格但斯克大学）；The University of Queensland（昆士兰大学）；Macquarie University（麦考瑞大学）；Alpine Quantum Technologies GmbH（阿尔卑斯量子技术有限公司）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes
QuTech, Delft University of Technology（代尔夫特理工大学量子技术研究所）；Quantum and Computer Engineering Department, Delft University of Technology（代尔夫特理工大学量子与计算机工程系）；Freie Universität Berlin（柏林自由大学）；Virginia Tech（弗吉尼亚理工大学）
Imperial College London（帝国理工学院）；University of Oxford（牛津大学）；Columbia University（哥伦比亚大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
我们提出了一个家庭的AdS/CFT对应的一种新的构造的量子纠错码的张量网络结构的基础上，完全可解的玩具模型。我们的构建块是一种特殊类型的张量与最大的纠缠沿任何bipartition，这引起了一个等距从散装希尔伯特空间的边界希尔伯特空间。整个张量网络是量子纠错码的编码器，其中体自由度和边界自由度可以分别被标识为逻辑自由度和物理自由度。这些模型捕捉到了AdS/CFT对应中纠缠的关键特征;特别是，Ryu-Takayanagi公式和三方信息的负性在许多情况下都完全遵守。体逻辑算子可以在多个边界区域上表示，这模拟了从体算子重构边界算子的Rindler-wedge重构，明确实现了Almheiri等人最近提出的AdS/CFT的量子纠错特性. al in arXiv：1411.7041.
Holographic duality between bulk topological order and boundary mixed-state order
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算科学联合中心）；Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气与计算机工程系）；Department of Physics, Northeastern University（东北大学物理系）
