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Tensor network states are used extensively as a mathematically convenient description of physically relevant states of many-body quantum systems.
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G. Aubrun, I. Nechita. Realigning random states. J. Math. Phys
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W. Brown, O. Fawzi. Scrambling speed of random quantum circuits. Preprint
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A. Cichocki, N. Lee, I. Oseledets, A.H. Phan, Q. Zhao, D.P. Mandic. Tensor networks for dimensionality reduction and large-scale optimizations: Part 2 applications and future perspectives. Found. Trends Machine Learning
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W. Brown, O. Fawzi. Decoupling with random quantum circuits. Commun. Math. Phys
2015
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Z. Landau, U. Vazirani, T. Vidick. A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians. Nature Physics
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A. Anshu, I. Arad, T. Vidick. A simple proof of the detectability lemma and spectral gap amplification. Phys. Rev. B
2016
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M. Bachmayr, R. Schneider, A. Uschmajew. Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Found. Comput. Math
2016
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F.G.S.L. Brandão, A.W. Harrow, M. Horodecki. Local random quantum circuits are approximate polynomial-designs. Commun. Math. Phys
2016
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D. Gosset, Y. Huang. Correlation length versus gap in frustration-free systems. Phys. Rev. Lett
2016
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J. Haah, A. Nahum, S. Vijay. Operator spreading in random unitary dynamics. Phys. Rev. X
2018
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J. Haah, M.B. Hastings, R. Kothari, G.H. Low. Quantum algorithm for simulating real time evolution of lattice Hamiltonians. Proc. IEEE 59th Annual Symposium on Foundations of Computer Science
2018
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A. Harrow, S. Mehraban. Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates. Preprint
2018
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M.J. Kastoryano, A. Lucia. Divide and conquer method for proving gaps of frustration-free Hamiltonians. J. Stat. Phys
2018
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G. Carleo, J.I. Cirac, K. Cranmer, L.Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, L. Zdeborová. Machine learning and the physical sciences. Rev. Mod. Phys
2019
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J.J. García-Ripoll. Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations. Preprint
2019
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M. Lemm. Gaplessness is not generic for translation-invariant spin chains. Preprint
2019
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M. Michałek, T. Seynnaev, F. Verstraete. A tensor version of the quantum Wielandt theorem. SIAM J. Matrix Anal. Appl
2019
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J.I. Cirac, D. Pérez-García, N. Schuch, F. Verstraete. Matrix product states and projected entangled pair states: Concepts, symmetries, and theorems. Preprint
2020
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S. Mugel, C. Kuchkovsky, E. Sanchez, S. Fernandez-Lorenzo, J. Luis-Hita, E. Lizaso, R. Orus. Dynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networks. Preprint
2020
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