Residual matrix product state for machine learning by Ye-Ming Meng, Jing Zhang, Peng Zhang, Chao Gao, Shi-Ju Ran

“…Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. …”
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Tensor computing for big data analytic by Ong, Jenn Bing

“…The rationale behind this thesis is to explore new applications of tensor network computing in the big data deep learning era. …”
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The large N limit of icMERA and holography by José J. Fernández-Melgarejo, Javier Molina-Vilaplana

“…Abstract In this work, we compute the entanglement entropy in continuous icMERA tensor networks for large N models at strong coupling. …”
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Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD by Jacques Bloch, Robert Lohmayer

“…We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. …”
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Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space by Oliver Kaestle, Regina Finsterhoelzl, Andreas Knorr, Alexander Carmele

“…Based on tensor-network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. …”
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Dynamical topological excitations in parafermion chains by Vilja Kaskela, J. L. Lado

“…Here, by using a combination of tensor network and kernel polynomial techniques, we demonstrate the emergence of zero modes and finite energy excitations in many-body parafermion chains. …”
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Variational quantum eigensolver with fewer qubits by Jin-Guo Liu, Yi-Hong Zhang, Yuan Wan, Lei Wang

“…One can obtain a tensor network representation of the ground state using a number of qubits smaller than the physical degrees of freedom. …”
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Universal thermodynamics in the Kitaev fractional liquid by Han Li, Dai-Wei Qu, Hao-Kai Zhang, Yi-Zhen Jia, Shou-Shu Gong, Yang Qi, Wei Li

“…With recently developed exponential tensor-network approach, we clear the pathway and perform finite-temperature simulations of the extended Kitaev model with additional interactions common in real materials. …”
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Contracting projected entangled pair states is average-case hard by Jonas Haferkamp, Dominik Hangleiter, Jens Eisert, Marek Gluza

“…In recent years, the tensor network ansatz has established itself as one of the most promising approaches enabling striking efficiency of simulating static properties of one-dimensional systems and abounding numerical applications in condensed matter theory. …”
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Estimating the randomness of quantum circuit ensembles up to 50 qubits by Minzhao Liu, Junyu Liu, Yuri Alexeev, Liang Jiang

“…Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.…”
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Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model by Satoshi Morita, Hyun-Yong Lee, Kedar Damle, Naoki Kawashima

“…We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity z, an aligning dimer-dimer interaction u that favors columnar order, and an attractive dimer-dimer interaction v between two adjacent dimers that lie on the same principal axis of the lattice. …”
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Hubbard model on the Bethe lattice via variational uniform tree states: Metal-insulator transition and a Fermi liquid by Peter Lunts, Antoine Georges, E. Miles Stoudenmire, Matthew Fishman

“…For this purpose, we introduce and develop the “variational uniform tree state” (VUTS) algorithm, a tensor-network algorithm which generalizes the variational uniform matrix product state algorithm to tree tensor networks. …”
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Entanglement and Chaos in Quantum Field Theory and Gravity by Wei, Annie Y.

“…We study toy models that consist of putting a lattice gauge theory on a tensor network, and we show how such toy models can be made background-independent. …”
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Classically optimized Hamiltonian simulation by Conor Mc Keever, Michael Lubasch

“…We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. …”
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Quantum Compressive Sensing: Mathematical Machinery, Quantum Algorithms, and Quantum Circuitry by Kyle M. Sherbert, Naveed Naimipour, Haleh Safavi, Harry C. Shaw, Mojtaba Soltanalian

“…Recent efforts in the literature consider instead a data-driven approach, training tensor networks to learn the structure of signals of interest. …”
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Grassmann time-evolving matrix product operators for equilibrium quantum impurity problems by Ruofan Chen, Xiansong Xu, Chu Guo

“…Tensor-network-based methods are promising candidates to solve quantum impurity problems (QIP). …”
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Holographic measurement and bulk teleportation by Stefano Antonini, Gregory Bentsen, ChunJun Cao, Jonathan Harper, Shao-Kai Jian, Brian Swingle

“…Using a bulk calculation in AdS 3 and tensor network models of holography (in particular, the HaPPY code and random tensor networks), we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of A and the state we project onto. …”
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Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order by Gu, Zheng-Cheng, Wen, Xiao-Gang

“…We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. …”
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Modular matrices as topological order parameter by a gauge-symmetry-preserved tensor renormalization approach by He, Huan, Moradi, Heidar, Wen, Xiao-Gang

“…In this paper, we will introduce a systematic numerical method based on tensor network to calculate modular matrices in two-dimensional systems, which can fully identify topological order with gapped edge. …”
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On the renormalization group fixed point of the two-dimensional Ising model at criticality by Alexander Stottmeister, Tobias J. Osborne

“…In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. …”
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