Tensor Networks, AdS/CFT Correspondence, and QuantumSecret Sharing Schemes

Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network - AdS/CFT connection is the association of a graph geometry with the tensor network. In the context of the AdS/CFT correspondence tensor network models have so far been limited to describing static spacetimes. In this thesis we look to extend tensor network models of AdS/CFT by describing the geometry of a dynamic spacetime using a tensor network. We provide a review of tensor networks in the context of AdS/CFT to motivate this extension, before proposing modifications of holographic tensor network models that capture features of AdS/CFT with dynamic spacetimes. This thesis includes the results of arXiv submission 1611.06220, along with a review of the relevant literature.Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network - AdS/CFT connection is the association of a graph geometry with the tensor network. In the context of the AdS/CFT correspondence tensor network models have so far been limited to describing static spacetimes. In this thesis we look to extend tensor network models of AdS/CFT by describing the geometry of a dynamic spacetime using a tensor network. We provide a review of tensor networks in the context of AdS/CFT to motivate this extension, before proposing modifications of holographic tensor network models that capture features of AdS/CFT with dynamic spacetimes. This thesis includes the results of arXiv submission 1611.06220, along with a review of the relevant literature.

arXiv:1709.09787Sep 28, 20172 citations

Holographic Tensor Networks in Full AdS/CFT

Ning Bao, Geoff Penington, Jonathan Sorce +1 more

We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large- $N$ CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.

arXiv:1902.10157Feb 26, 201925 citations

Quantum Critical Systems and AdS/CFT

Horaƫiu Năstase

Cambridge University Press eBooksSep 21, 20170 citations

Tensor networks for quantum computing

A. V. Berezutskii, Minzhao Liu, Atithi Acharya +25 more

arXiv:2503.08626Nature Reviews PhysicsJul 30, 202521 citations

6.S899 Project Report Tensor Networks, Quantum Error Correction, and AdS/CFT

John C. Napp

In recent years, the high energy physics community has become increasingly interested in entanglement, especially since it seems that, in some sense, spacetime itself may arise from entanglement [1]. Since dealing with entanglement is a strong point of quantum information theory, it’s perhaps not surprising that quantum information is working its way into some work in this area, including work in the context of the AdS/CFT correspondence, a duality between quantum theories of gravity in d + 1 dimensions and conformal field theories in d dimensions. In this report, I survey at a very schematic level some recent work which lies in the intersection of quantum information theory (broadly speaking) and the AdS/CFT correspondence, especially in relation to tensor network models of holography. For completion, I won’t assume background which wasn’t covered in class, and so I briefly review relevant features of AdS/CFT and tensor networks.In recent years, the high energy physics community has become increasingly interested in entanglement, especially since it seems that, in some sense, spacetime itself may arise from entanglement [1]. Since dealing with entanglement is a strong point of quantum information theory, it’s perhaps not surprising that quantum information is working its way into some work in this area, including work in the context of the AdS/CFT correspondence, a duality between quantum theories of gravity in d + 1 dimensions and conformal field theories in d dimensions. In this report, I survey at a very schematic level some recent work which lies in the intersection of quantum information theory (broadly speaking) and the AdS/CFT correspondence, especially in relation to tensor network models of holography. For completion, I won’t assume background which wasn’t covered in class, and so I briefly review relevant features of AdS/CFT and tensor networks.

Jan 1, 20150 citations

We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-

N

CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.