Hand-waving and interpretive dance: an introductory course on tensor networks

By Jacob C. Bridgeman, Christopher T. Chubb. 2016

477 citations recorded by the source corpus.

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/11fd785de2ccc5dabf2000177e320204c58deb33

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Citations in the corpus

Efficient representation of quantum many-body states with deep neural networks (2017, unknown): “Using the above theorem, we now construct efficient DBM representation of any tensor network states, which include the PEPS and the MERA states as special cases [4, 25, 26].”
Quantum error mitigation (2022, methodology): “The proof here uses tensor network notations (Bridgeman and Chubb, 2017) and it can be easily extended to more copies and/or with O acting on the m th copy rather than the first.”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “While there are many reviews on that topic (Biamonte, 2019; Bridgeman and Chubb, 2017; Cirac and Verstraete, 2009; Hallberg, 2006; Orus, 2014; Schollwöck, 2005, 2011; Verstraete et al., 2008) the vast majority focus on the practical aspects of tensor networks; in particular, on how to use them in…”