Sign Problem in Tensor-Network Contraction by Jielun Chen, Jiaqing Jiang, Dominik Hangleiter, Norbert Schuch

“…We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. …”
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Hybrid Tree Tensor Networks for Quantum Simulation by Julian Schuhmacher, Marco Ballarin, Alberto Baiardi, Giuseppe Magnifico, Francesco Tacchino, Simone Montangero, Ivano Tavernelli

“…Hybrid tensor networks (hTNs) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. …”
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Quantum metrology using quantum combs and tensor network formalism by Stanisław Kurdziałek, Piotr Dulian, Joanna Majsak, Sagnik Chakraborty, Rafał Demkowicz-Dobrzański

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Reflected entropy in random tensor networks. Part III. Triway cuts by Chris Akers, Thomas Faulkner, Simon Lin, Pratik Rath

“…Abstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. …”
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Overlapping qubits from non-isometric maps and de Sitter tensor networks by ChunJun Cao, Wissam Chemissany, Alexander Jahn, Zoltán Zimborás

“…For a concrete example, we construct two tensor network models of de Sitter space-time, demonstrating how exponential expansion and local physics can be spoofed for a long period before breaking down. …”
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Cross-Shaped Heat Tensor Network for Morphometric Analysis Using Zebrafish Larvae Feature Keypoints by Xin Chai, Tan Sun, Zhaoxin Li, Yanqi Zhang, Qixin Sun, Ning Zhang, Jing Qiu, Xiujuan Chai

“…We propose the cross-shaped heat tensor network (CSHT-Net), a feature point detection framework consisting of a novel keypoint training method named cross-shaped heat tensor and a feature extractor called combinatorial convolutional block. …”
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Relation Classification via Recurrent Neural Network with Attention and Tensor Layers by Runyan Zhang, Fanrong Meng, Yong Zhou, Bing Liu

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Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models by Anupam Mitra, Tameem Albash, Philip Daniel Blocher, Jun Takahashi, Akimasa Miyake, Grant Biedermann, Ivan H Deutsch

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Fault-tolerant quantum memory using low-depth random circuit codes by Jon Nelson, Gregory Bentsen, Steven T. Flammia, Michael J. Gullans

“…Replacing the tensor network with a so-called “tropical” tensor network, we also show how to perform minimum weight decoding. …”
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Quantum-inspired fluid simulation of two-dimensional turbulence with GPU acceleration by Leonhard Hölscher, Pooja Rao, Lukas Müller, Johannes Klepsch, Andre Luckow, Tobias Stollenwerk, Frank K. Wilhelm

“…Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. …”
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Growth of a Renormalized Operator as a Probe of Chaos by Xing Huang, Binchao Zhang

“…The first one is a MERA-like tensor network built from a random unitary circuit with the operator size defined using the integrated out-of-time-ordered correlator (OTOC). …”
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Simulating quantum circuits using the multi-scale entanglement renormalization ansatz by A. V. Berezutskii, I. A. Luchnikov, A. K. Fedorov

“…Here, we propose a scalable technique for approximate simulations of intermediate-size quantum circuits on the basis of the multi-scale entanglement renormalization ansatz (MERA) and Riemannian optimization. The MERA is a tensor network, whose geometry together with orthogonality constraints imposed on its tensors allow approximating many-body quantum states lying beyond the area-law scaling of the entanglement entropy. …”
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Recursive Quantum Relaxation for Combinatorial Optimization Problems by Ruho Kondo, Yuki Sato, Rudy Raymond, Naoki Yamamoto

“…Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO not only outperforms the Goemans-Williamson and recursive QAOA methods, but also is comparable to state-of-the-art classical solvers. …”
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Projected entangled pair states with flexible geometry by Siddhartha Patra, Sukhbinder Singh, Román Orús

“…Our paper opens the way to apply tensor network algorithms to arbitrary, even fluctuating, background geometries.…”
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Exact projected entangled pair ground states with topological Euler invariant by Thorsten B. Wahl, Wojciech J. Jankowski, Adrien Bouhon, Gaurav Chaudhary, Robert-Jan Slager

“…These PEPS thus form the first tensor network representative of a non-interacting, gapped two-dimensional topological phase, similar to the Kitaev chain in one dimension. …”
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Parallelizing Quantum Simulation With Decision Diagrams by Shaowen Li, Yusuke Kimura, Hiroyuki Sato, Masahiro Fujita

“…However, their advantage of memory efficiency does not let it replace the mainstream statevector and tensor network-based approaches. We argue the reason is the lack of effective parallelization strategies in performing calculations on DDs. …”
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A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity by Ryan L'Abbate, Anthony D'Onofrio, Samuel Stein, Samuel Yen-Chi Chen, Ang Li, Pin-Yu Chen, Juntao Chen, Ying Mao

“…The classical component employs a tensor network for compression and feature extraction, enabling higher dimensional data to be encoded onto logical quantum circuits with limited qubits. …”
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Interpreting convolutional neural networks' low-dimensional approximation to quantum spin systems by Yilong Ju, Shah Saad Alam, Jonathan Minoff, Fabio Anselmi, Han Pu, Ankit Patel

“…For the final part of the puzzle, inspired by similar analyses for matrix product states and tensor networks, we show that the CNNs rely on the spectrum of each subsystem's entanglement Hamiltonians as captured by the size of the convolutional filter. …”
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Classical and quantum algorithms for many-body problems by Ayral, Thomas

“…In particular, we begin by showing how tensor networks, often used as reference tools to gauge the interest of quantum methods, can also be used to initialize a quantum computation, in addition to simulating it realistically. …”
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Entanglement negativity and replica symmetry breaking in general holographic states by Xi Dong, Jonah Kudler-Flam, Pratik Rath

“…Abstract The entanglement negativity E $$ \mathcal{E} $$ (A : B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity E 2 k $$ {\mathcal{E}}^{(2k)} $$ generically break the ℤ 2k replica symmetry. …”
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