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Tensor Network Algorithms: a Route Map

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arxiv 2205.10345 v2 pith:X474YDZ5 submitted 2022-05-20 quant-ph

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keywords tensorideaslastnetworknetworkssomealgorithmicalgorithms
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Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially the last ten years have seen an explosion of new ideas and results that may be overwhelming for the newcomer. This short review introduces the basic ideas, the best established methods and some of the most significant algorithmic developments that are expanding the boundaries of the tensor network potential. The goal is to help the reader not only appreciate the many possibilities offered by tensor networks, but also find their way through state-of-the-art codes, their applicability and some avenues of ongoing progress.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum computation of hadron scattering in a lattice gauge theory

    quant-ph 2025-05 conditional novelty 6.0 of 10

    On a trapped-ion quantum computer, the authors prepared multiple meson wave packets and simulated their early-time collisions in a 1+1D Z2 lattice gauge theory.

  2. Observation of Robust and Coherent Non-Abelian Hadron Dynamics on Noisy Quantum Processors

    hep-lat 2026-02 reject novelty 5.0 of 10

    A 60-site SU(2) lattice gauge theory was run on 120 qubits, but the implemented dynamics approximate to non-interacting fermion hopping, and the abstract's claimed breathing-mode frequency is not extracted anywhere.

  3. Initial tensor construction for the tensor renormalization group

    hep-lat 2025-01 conditional novelty 4.0 of 10

    A delta-function index-shifting algorithm builds locally connected initial tensors for the tensor renormalization group from arbitrary Boltzmann factors, and boundary-style squeezers remove the initial-tensor dependen...

  4. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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