Complexity, action, and black holes by Brown, Adam R., Susskind, Leonard, Swingle, Brian, Zhao, Ying, Roberts, Daniel Adam

“…We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.…”
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CHAOS, holography, and other science by Roberts, Daniel Adam

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Polarity and subjectivity detection with multitask learning and BERT embedding by Satapathy, Ranjan, Pardeshi, Shweta Rajesh, Cambria, Erik

“…To ensure high-quality knowledge sharing between the tasks, we use the Neural Tensor Network, which consists of a bilinear tensor layer that links the two entity vectors. …”
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Compressing deep neural networks by matrix product operators by Ze-Feng Gao, Song Cheng, Rong-Qiang He, Z. Y. Xie, Hui-Hai Zhao, Zhong-Yi Lu, Tao Xiang

“…Here we show that this problem can be effectively solved by representing linear transformations with matrix product operators (MPOs), which is a tensor network originally proposed in physics to characterize the short-range entanglement in one-dimensional quantum states. …”
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Using the Environment to Understand non-Markovian Open Quantum Systems by Dominic Gribben, Aidan Strathearn, Gerald E. Fux, Peter Kirton, Brendon W. Lovett

“…In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. …”
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Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase by Alexander Wietek, Philippe Corboz, Stefan Wessel, B. Normand, Frédéric Mila, Andreas Honecker

“…The second is the use of tensor-network methods, in the form of infinite projected entangled-pair states (iPEPS), for the calculation of finite-temperature quantities. …”
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Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice by Francesco Ferrari, Sen Niu, Juraj Hasik, Yasir Iqbal, Didier Poilblanc, Federico Becca

“…By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for $J_D/J \gtrsim 0.03 \mathrm{-} 0.04$; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for $J_D \to 0$. …”
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Topological Phases of an Interacting Majorana Benalcazar–Bernevig–Hughes Model by Alfonso Maiellaro, Fabrizio Illuminati, Roberta Citro

“…We consider an interacting strip of four chains of length <i>L</i> and perform a density matrix renormalization group (DMRG) numerical simulation based on a tensor-network approach. Study of the non-local fermionic correlations and the degenerate entanglement spectrum indicates that the topological phases are robust in the presence of interactions, even in the strongly interacting regime.…”
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Twice upon a time: timelike-separated quantum extremal surfaces by Netta Engelhardt, Geoff Penington, Arvin Shahbazi-Moghaddam

“…Notably, our proposal suggests that the gravitational analogue of a tensor network is not necessarily the time-reflection symmetric slice, even when one exists.…”
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Unifying projected entangled pair state contractions by Michael Lubasch, J Ignacio Cirac, Mari-Carmen Bañuls

“…The approximate contraction of a tensor network of projected entangled pair states (PEPS) is a fundamental ingredient of any PEPS algorithm, required for the optimization of the tensors in ground state search or time evolution, as well as for the evaluation of expectation values. …”
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Phenomenological theory of variational quantum ground-state preparation by Nikita Astrakhantsev, Guglielmo Mazzola, Ivano Tavernelli, Giuseppe Carleo

“…The variational quantum eigensolver algorithm aims to prepare the ground state of a Hamiltonian exploiting parametrized quantum circuits that may offer an advantage compared to classical trial states used, for instance, in quantum Monte Carlo or tensor network calculations. While, traditionally, the main focus has been on developing better trial circuits, we show that the algorithm's success, if optimized within stochastic gradient descent (SGD) or quantum natural gradient descent (QNGD), crucially depends on other parameters such as the learning rate, the number N_{s} of measurements to estimate the gradient components, and the Hamiltonian gap Δ. …”
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Flat entanglement spectra in fixed-area states of quantum gravity by Dong, Xi, Harlow, Daniel, Marolf, Donald

“…This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of alge- braic centers which arise in the quantum error-correcting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh.…”
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Efficient classical algorithms for simulating symmetric quantum systems by Anschuetz, Eric R., Bauer, Andreas, Kiani, Bobak T., Lloyd, Seth

“…Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. …”
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The structure of many-body entanglement by Swingle, Brian Gordon

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Topological Phase Diagram of an Interacting Kitaev Chain: Mean Field versus DMRG Study by Giovanni Nunziante, Alfonso Maiellaro, Claudio Guarcello, Roberta Citro

“…We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. …”
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Absorbing phase transition with a continuously varying exponent in a quantum contact process: A neural network approach by Minjae Jo, Jongshin Lee, K. Choi, B. Kahng

“…Numerical simulations using the quantum jump Monte Carlo technique and tensor network method are performed to determine all the other critical exponents of the QCP. …”
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Single-hole spectra of Kitaev spin liquids: from dynamical Nagaoka ferromagnetism to spin-hole fractionalization by Wilhelm Kadow, Hui-Ke Jin, Johannes Knolle, Michael Knap

“…In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. …”
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Linear to multi-linear algebra and systems using tensors by Divyanshu Pandey, Adithya Venugopal, Harry Leib

“…In addition, this study also introduces the notion of contracted convolution for both discrete and continuous multi-linear system tensors. Tensor network representation of various tensor operations is also presented. …”
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Preparing valence-bond-solid states on noisy intermediate-scale quantum computers by Bruno Murta, Pedro M. Q. Cruz, J. Fernández-Rossier

“…We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. …”
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Superfluid density and quasi-long-range order in the one-dimensional disordered Bose–Hubbard model by M Gerster, M Rizzi, F Tschirsich, P Silvi, R Fazio, S Montangero

“…We study the equilibrium properties of the one-dimensional disordered Bose–Hubbard model by means of a gauge-adaptive tree tensor network variational method suitable for systems with periodic boundary conditions. …”
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