Coarse graining of spin net models: dynamics of intertwiners by Bianca Dittrich, Mercedes Martín-Benito, Erik Schnetter

“…For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model.…”
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Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface by J. L. Lado, M. Sigrist

“…This genuine many-body problem is solved exactly by employing a combination of kernel polynomial and tensor network techniques. We unveil the nature of such zero modes by showing that they can be adiabatically connected to solitonic solutions between a superconductor and a mean-field antiferromagnet. …”
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Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm by Benjamin F. Schiffer, Jordi Tura, J. Ignacio Cirac

“…We benchmark for a nonintegrable spin-1/2 transverse and longitudinal Ising chain with N=53 sites using tensor-network techniques. Using a black-box gradient-based approach, we report a reduction in the total evolution time for a given desired ground-state fidelity by a factor of 10, which makes our method suitable for the limited decoherence time of noisy-intermediate scale quantum devices.…”
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Enhancing combinatorial optimization with classical and quantum generative models by Javier Alcazar, Mohammad Ghazi Vakili, Can B. Kalayci, Alejandro Perdomo-Ortiz

“…We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. …”
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Entanglement renormalization of a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed CFT by B. Cardona, J. Molina-Vilaplana

“…Abstract In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a T T ¯ $$ \overline{T} $$ -deformed scalar CFT on the line, to first order in the deformation parameter. …”
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Evidence of a spin liquid with hard-core bosons in a square lattice by Y-H Chan, L-M Duan

“…We numerically investigated the phase diagram of the J _1 – J _2 XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and found strong evidence that in the intermediate region around J _2 / J _1  ∼ 0.5, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Néel state on the J _2  ≪  J _1 side and the stripe antiferromagnetic phase on the J _2  ≫  J _1 side. …”
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Entanglement in the quantum phases of an unfrustrated Rydberg atom array by Matthew J. O’Rourke, Garnet Kin-Lic Chan

“…However, the native long-range interactions between the atoms complicate experimental analysis and precise theoretical understanding of these systems. Here we use new tensor network algorithms capable of including all long-range interactions to study the ground state phase diagram of Rydberg atoms in a geometrically unfrustrated square lattice array. …”
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Nonliquid cellular states: Gluing gauge-higher-symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects by Juven Wang

“…This approach shows gluing the familiar extended topological quantum field theory or conformal field theory data via topology, geometry, and renormalization consistency criteria (via certain modified group cohomology or cobordism theory data) in a tensor network can still guide us to analyze the nonliquid states. …”
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Learning Feynman Diagrams with Tensor Trains by Yuriel Núñez Fernández, Matthieu Jeannin, Philipp T. Dumitrescu, Thomas Kloss, Jason Kaye, Olivier Parcollet, Xavier Waintal

“…We use tensor network techniques to obtain high-order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. …”
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Entanglement of purification: from spin chains to holography by Phuc Nguyen, Trithep Devakul, Matthew G. Halbasch, Michael P. Zaletel, Brian Swingle

“…We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.…”
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Controlling magnetic correlations in a driven Hubbard system far from half-filling by Gao, H, Coulthard, JR, Jaksch, D, Mur-Petit, J

“…We then demonstrate numerically using tensor network methods for a one-dimensional (1D) lattice that a slow modification of the driving strength allows near-adiabatic transfer of the system from the ground state of the underlying Hubbard model to the ground state of the effective t−J Hamiltonian. …”

Categorical Quantum Circuits by Bergholm, V, Biamonte, J

“…Our specific approach has further applications in applying category theory and related ideas to tensor network simulation.…”

Entanglement entropy production in Quantum Neural Networks by Marco Ballarin, Stefano Mangini, Simone Montangero, Chiara Macchiavello, Riccardo Mengoni

“…However, quantitative studies of the QNN-generated entanglement have been investigated only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. …”
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Stabilizer entropies and nonstabilizerness monotones by Tobias Haug, Lorenzo Piroli

“…Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. …”
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Controlling quantum many-body systems using reduced-order modeling by I. A. Luchnikov, M. A. Gavreev, A. K. Fedorov

“…The method employs a tensor-network scheme to construct a reduced-order model of a subsystem's non-Markovian dynamics. …”
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Efficient separation of quantum from classical correlations for mixed states with a fixed charge by Christian Carisch, Oded Zilberberg

“…Moreover, it can be efficiently computed using a tensor network representation of the state's density matrix. …”
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TensorCircuit: a Quantum Software Framework for the NISQ Era by Shi-Xin Zhang, Jonathan Allcock, Zhou-Quan Wan, Shuo Liu, Jiace Sun, Hao Yu, Xing-Han Yang, Jiezhong Qiu, Zhaofeng Ye, Yu-Qin Chen, Chee-Kong Lee, Yi-Cong Zheng, Shao-Kai Jian, Hong Yao, Chang-Yu Hsieh, Shengyu Zhang

“…TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. …”
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Towards explicit discrete holography: Aperiodic spin chains from hyperbolic tilings by Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, Zhuo-Yu Xian

“…The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. …”
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Living on the edge: a toy model for holographic reconstruction of algebras with centers by William Donnelly, Donald Marolf, Ben Michel, Jason Wien

“…The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. …”
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Neural network enhanced hybrid quantum many-body dynamical distributions by Rouven Koch, Jose L. Lado

“…Here we show that the combination of machine-learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. …”
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