PIRSA:08040047

Quantum information, graphs, and statistical mechanics

Van den Nest, M. (2008). Quantum information, graphs, and statistical mechanics . Perimeter Institute. https://pirsa.org/08040047

Van den Nest, Maarten. Quantum information, graphs, and statistical mechanics . Perimeter Institute, Apr. 28, 2008, https://pirsa.org/08040047 

          @misc{ pirsa_PIRSA:08040047,
            doi = {10.48660/08040047},
            url = {https://pirsa.org/08040047},
            author = {Van den Nest, Maarten},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum information, graphs, and statistical mechanics },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {apr},
            note = {PIRSA:08040047 see, \url{https://pirsa.org}}
          }

Maarten Van den Nest

Universität Innsbruck

Talk number
PIRSA:08040047
Collection
Talk Type
Subject
Abstract
We give an overview of several connections between topics in quantum information theory, graph theory, and statistical mechanics. The central concepts are mappings from statistical mechanical models defined on graphs, to entangled states of multi-party quantum systems. We present a selection of such mappings, and illustrate how they can be used to obtain a cross-fertilization between different research areas. For example, we show how width parameters in graph theory such as \'tree-width\' and \'rank-width\', which may be used to assess the computational hardness of evaluating partition functions, are intimately related with the entanglement measure \'entanglement width\', which is used to asses to computational power of resource states in quantum information. Furthermore, using our mappings we provide simple techniques to relate different statistical mechanical models with each other via basic graph transformations. These techniques can be used to prove that that there exist models which are \'complete\' in the sense that every other model can be viewed as a special instance of such a complete model via a polynomial reduction. Examples of such complete models include the 2D Ising model in an external field, as well as the zero-field 3D Ising model. Joint work with W. Duer, G. de las Cuevas, R. Huebener and H. Briegel