Concatenated tensor network states

Abstract

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.

16 pages, 4 figures

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• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Entanglement negativity in the critical Ising chain
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Entanglement entropy of two disjoint intervals in c=1 theories
• Entanglement negativity and conformal field theory: a Monte Carlo study
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• A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
• Predicting toxicity by quantum machine learning
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