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      A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

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          Abstract

          This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.

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          Persistent entanglement in arrays of interacting particles

          We study the entanglement properties of a class of N qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They have also a high {\em persistency of entanglement} which means that N/2 qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of other multi-particle entangled states such as the generalized GHZ states of \(
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            Efficient classical simulation of slightly entangled quantum computations

            (2003)
            We present a scheme to efficiently simulate, with a classical computer, the dynamics of multipartite quantum systems on which the amount of entanglement (or of correlations in the case of mixed-state dynamics) is conveniently restricted. The evolution of a pure state of n qubits can be simulated by using computational resources that grow linearly in n and exponentially in the entanglement. We show that a pure-state quantum computation can only yield an exponential speed-up with respect to classical computations if the entanglement increases with the size n of the computation, and gives a lower bound on the required growth.
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              DMRG and periodic boundary conditions: a quantum information perspective

              We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which the results are dramatically improved. The picture also explains some features of the method in terms of entanglement and teleportation.
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                Author and article information

                Journal
                10 June 2013
                2014-06-10
                Article
                10.1016/j.aop.2014.06.013
                1306.2164
                5f136414-9b4e-46d0-9581-c3cdb150c0b6

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Annals of Physics 349 (2014) 117-158
                51 pages, 45 figures, minor typos corrected. Accepted for publication in Annals of Physics
                cond-mat.str-el hep-lat hep-th quant-ph

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