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Classical simulation of quantum many-body systems is a fundamental challenge due to their exponentially large Hilbert spaces.
Y. Huang, “2D Local Hamiltonian with area laws is QMA-complete,” in 2020 IEEE International Symposium on Information Theory , 2020, pp. 1927–1932
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M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics , vol. 144, no. 3, pp. 443–490, 1992
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C. Holzhey, F. Larsen, and F. Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nuclear Physics B , vol. 424, no. 3, pp. 443–467, 1994
1994
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Y. Huang, “Computing local properties in the trivial phase,” arXiv:2001.10763
2001
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G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, “Entanglement in quantum critical phenomena,” Physical Review Letters , vol. 90, no. 22, p. 227902, 2003
2003
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F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “Matrix product density operators: Simulation of finite-temperature and dissipative systems,” Physical Review Letters , vol. 93, no. 20, p. 207204, 2004
2004
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M. Zwolak and G. Vidal, “Mixed-state dynamics in one-dimensional quantum lattice systems: A time-dependent superoperator renormalization algorithm,” Physical Review Letters , vol. 93, no. 20, p. 207205, 2004
2004
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J. I. Latorre, E. Rico, and G. Vidal, “Ground state entanglement in quantum spin chains,” Quantum Information and Computation , vol. 4, no. 1, pp. 48–92, 2004
2004
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P. Calabrese and J. Cardy, “Entanglement entropy and quantum field theory,” Journal of Statistical Mechanics: Theory and Experiment , vol. 2004, no. 06, p. P06002, 2004
2004
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M. M. Wolf, “Violation of the entropic area law for fermions,” Physical Review Letters , vol. 96, no. 1, p. 010404, 2006
2006
Cited alongside, same era.
D. Gioev and I. Klich, “Entanglement entropy of fermions in any dimension and the Widom conjecture,” Physical Review Letters , vol. 96, no. 10, p. 100503, 2006
2006
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D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix product state representations,” Quantum Information and Computation , vol. 7, no. 5-6, pp. 401–430, 2007
2007
Cited alongside, same era.
M. B. Hastings, “An area law for one-dimensional quantum systems,” Journal of Statistical Mechanics: Theory and Experiment , vol. 2007, no. 08, p. P08024, 2007
2007
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G. Vidal, “Classical simulation of infinite-size quantum lattice systems in one spatial dimension,” Physical Review Letters , vol. 98, no. 7, p. 070201, 2007
Z. Landau, U. Vazirani, and T. Vidick, “A polynomial time algorithm for the ground state of one-dimensional gapped local Hamiltonians,” Nature Physics , vol. 11, no. 7, pp. 566–569, 2015
2015
Later among the works it cites.
S. Gharibian, Y. Huang, Z. Landau, and S. W. Shin, “Quantum Hamiltonian complexity,” Foundations and Trends in Theoretical Computer Science , vol. 10, no. 3, pp. 159–282, 2015
2015
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Y. Huang, “Classical simulation of quantum many-body systems,” Ph.D. dissertation, University of California, Berkeley, 2015
2015
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C. T. Chubb and S. T. Flammia, “Computing the degenerate ground space of gapped spin chains in polynomial time,” Chicago Journal of Theoretical Computer Science , vol. 2016, p. 9, 2016
2016
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Y. Ge and J. Eisert, “Area laws and efficient descriptions of quantum many-body states,” New Journal of Physics , vol. 18, no. 8, p. 083026, 2016
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2007
Cited alongside, same era.
N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, “Entropy scaling and simulability by matrix product states,” Physical Review Letters , vol. 100, no. 3, p. 030504, 2008
2008
Cited alongside, same era.
——, “Entanglement entropy and conformal field theory,” Journal of Physics A: Mathematical and Theoretical , vol. 42, no. 50, p. 504005, 2009
2009
Cited alongside, same era.
J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Reviews of Modern Physics , vol. 82, no. 1, pp. 277–306, 2010
2010
Cited alongside, same era.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics , vol. 326, no. 1, pp. 96–192, 2011
2011
Cited alongside, same era.
T. J. Osborne, “Hamiltonian complexity,” Reports on Progress in Physics , vol. 75, no. 2, p. 022001, 2012
2012
Cited alongside, same era.
M. Kliesch, D. Gross, and J. Eisert, “Matrix-product operators and states: NP-hardness and undecidability,” Physical Review Letters , vol. 113, no. 16, p. 160503, 2014
2014
Cited alongside, same era.
F. Verstraete and J. I. Cirac, “Renormalization algorithms for quantum-many body systems in two and higher dimensions,” arXiv:cond-mat/0407066
Cited in the paper.
2016
Later among the works it cites.
I. Arad, Z. Landau, U. Vazirani, and T. Vidick, “Rigorous RG algorithms and area laws for low energy eigenstates in 1D,” Communications in Mathematical Physics , vol. 356, no. 1, pp. 65–105, 2017
2017
Later among the works it cites.
A. M. Dalzell and F. G. S. L. Brandão, “Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians,” Quantum , vol. 3, p. 187, 2019
2019
Closest in time.
Y. Huang, “Matrix product state approximations: Bringing theory closer to practice,” Quantum Views , vol. 3, p. 26, 2019
2019
Closest in time.
——, “Two-dimensional local Hamiltonian problem with area laws is QMA-complete,” Journal of Computational Physics , vol. 443, p. 110534, 2021
2021
Closest in time.
F. Verstraete and J. I. Cirac, “Matrix product states represent ground states faithfully,” Physical Review B , vol. 73, no. 9, p. 094423, 2006
2022
Closest in time.