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We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states.
1901
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G. Vidal, Efficient Simulation of One-Dimensional Quantum Many-Body Systems, Physical Review Letters 93
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P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, Journal of Statistical Mechanics: Theory and Experiment 2005
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T. Prosen and M. Žnidarič, Is the efficiency of classical simulations of quantum dynamics related to integrability?, Physical Review E 75
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I. P. McCulloch, From density-matrix renormalization group to matrix product states, Journal of Statistical Mechanics: Theory and Experiment 2007
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P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: A conformal field theory approach, Journal of Statistical Mechanics: Theory and Experiment 2007
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R. Orús and G. Vidal, Infinite time-evolving block decimation algorithm beyond unitary evolution, Physical Review B 78
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M. C. Bañuls, M. B. Hastings, F. Verstraete, and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains, Physical Review Letters 102
2009
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I. Pižorn and T. Prosen, Operator space entanglement entropy in $XY$ spin chains, Physical Review B 79
2009
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2009
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B. Pirvu, V. Murg, J. I. Cirac, and F. Verstraete, Matrix product operator representations, New Journal of Physics 12
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F. Verstraete and J. I. Cirac, Continuous Matrix Product States for Quantum Fields, Physical Review Letters 104
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Y.-K. Huang, Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices, Physical Review E 83
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M. Sonner, A. Lerose, and D. A. Abanin, Influence functional of many-body systems: Temporal entanglement and matrix-product state representation, Annals of Physics Special Issue on Philip W. Anderson, 435
2021
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2021
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M. Frías-Pérez and M. C. Bañuls, Light cone tensor network and time evolution, Physical Review B 106
2022
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G. Giudice, G. Giudici, M. Sonner, J. Thoenniss, A. Lerose, D. A. Abanin, and L. Piroli, Temporal Entanglement, Quasiparticles, and the Role of Interactions, Physical Review Letters 128
2022
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2012
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2012
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A. Coser, E. Tonni, and P. Calabrese, Entanglement negativity after a global quantum quench, Journal of Statistical Mechanics: Theory and Experiment 2014
2014
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2015
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2017
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A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, Nature Communications 9
2018
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2018
Cited alongside, same era.
2022
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2022
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A. Lerose, M. Sonner, and D. A. Abanin, Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality, Physical Review B 107
2023
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J. Thoenniss, A. Lerose, and D. A. Abanin, Nonequilibrium quantum impurity problems via matrix-product states in the temporal domain, Physical Review B 107
2023
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M. C. Bañuls, Tensor Network Algorithms: A Route Map, Annual Review of Condensed Matter Physics 14
2023
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2023
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2023
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X. Jiang, P. Wang, H. Wu, and H. Yang, Timelike entanglement entropy and $T\bar{ }
2023
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2023
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A. Foligno, T. Zhou, and B. Bertini, Temporal Entanglement in Chaotic Quantum Circuits, Physical Review X 13
2023
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