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Tensor networks take a central role in quantum physics as they can provide an efficient approximation to specific classes of quantum states. The associated graphical language can also easily describe and pictorially reason about quantum circuits, channels, protocols and open systems. In a recent study, A. Jahn and a research team in the departments of complex quantum systems, materials and energy and mathematics and computer science in Germany introduced a versatile and efficient framework to study tensor networks by extending previous tools. The researchers used bulk tiling (computing geometric technique) in their work to obtain highly accurate critical data and established a link between holographic quantum error-correcting codes and tensor networks. They expect the work to stimulate further investigations of tensor network models to capture bulk-boundary correspondences. The results are now published on Science Advances.
The AdS/CFT correspondence, which stands for anti-de Sitter/conformal field theory correspondence, is one of the largest areas of research in string theory, and is an example in the context of bulk-boundary dualities in which a holographic duality exists between gravity in a bulk space and a critical quantum field on its boundary. This correspondence that relates two very different theories was originally formulated by physicist Juan M. Maldacena in 1997, and is considered a significantly important result in string theory within the last 20 years.
Feature - Dualities - Relationship - Bulk - Geometry
A key feature of these dualities is the relationship between bulk geometry and boundary entanglement entropies, which physicists had previously illuminated using the Ryu-Takayanagi formula. Since it is important to understand entanglement in the context of AdS/CFT, researchers realized the necessity of tensor networks as an ideal framework to construct holographic toy models, such as the multiscale entanglement renormalization ansatz simulation (MERA). Physicists had previously explored the realization that quantum error correction could be facilitated by a holographic duality, which further connected...
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