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In recent years we've seen the birth of a new field known as hamiltonian complexity lying at the crossroads between computer science and theoretical physics.
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by same author, Locality in Quantum and Markov Dynamics on Lattices and Networks , (2004), no. 2, 4
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S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order , Phys. Rev. Lett. 97
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Sergey Bravyi, Efficient algorithm for a quantum analogue of 2 2 -SAT , quant-ph/0602108, 2006
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2006
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Matthew B. Hastings and Tohru Koma, Spectral Gap and Exponential Decay of Correlations , Comm. Math. Phys. 265
2006
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Yi-Kai Liu, Consistency of local density matrices is QMA-complete , Approximation, randomization and combinatorial optimization, Lecture Notes in Comput. Sci., vol. 4110, Springer, Berlin, 2006, pp. 438–449. MR 2305030 (2008a:68081)
2006
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Bruno Nachtergaele, Yoshiko Ogata, and Robert Sims, Propagation of correlations in quantum lattice systems , J. Stat. Phys. 124
2006
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Bruno Nachtergaele and Robert Sims, Lieb-Robinson Bounds and the Exponential Clustering Theorem , Comm. Math. Phys. 265
2006
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Tobias J. Osborne, Efficient Approximation of the Dynamics of One-Dimensional Quantum Spin Systems , Phys. Rev. Lett. 97
2006
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G. Vidal, A class of quantum many-body states that can be efficiently simulated , cond-mat/0610099, 2006
2006
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Christian K. Burrell and Tobias J. Osborne, Bounds on the Speed of Information Propagation in Disordered Quantum Spin Chains , Phys. Rev. Lett. 99
2007
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Paolo Buttà, Emanuele Caglioti, Sara Di Ruzza, and Carlo Marchioro, On the propagation of a perturbation in an anharmonic system , J. Stat. Phys. 127
2007
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Dorit Aharonov, Itai Arad, and Sandy Irani, Efficient algorithm for approximating one-dimensional ground states , Phys. Rev. A 82
2010
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by same author, Quantum Hamiltonian complexity and the detectability lemma , arXiv:1011.3445, 2010
2010
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Andris Ambainis, Julia Kempe, and Or Sattath, A Quantum Lovász Local Lemma , Proceedings of the 42nd ACM symposium on Theory of computing (New York, NY, USA), STOC ’10, ACM, 2010, pp. 151–160
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by same author, An area law for one-dimensional quantum systems , J. Stat. Mech. (2007), no. 8, P08024. MR 2338267 (2008h:82010)
2007
Cited alongside, same era.
Alastair Kay, Quantum-Merlin-Arthur-complete translationally invariant hamiltonian problem and the complexity of finding ground-state energies in physical systems , Phys. Rev. A 76
2007
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2007
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Yi-Kai Liu, Matthias Christandl, and F. Verstraete, Quantum Computational Complexity of the N {N} -Representability Problem: QMA Complete , Phys. Rev. Lett. 98
2007
Cited alongside, same era.
by same author, A multi-dimensional Lieb-Schultz-Mattis theorem , Comm. Math. Phys. 276
2007
Cited alongside, same era.
Daniel Nagaj and Shay Mozes, New construction for a QMA complete three-local Hamiltonian , J. Math. Phys. 48
2007
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by same author, Simulating adiabatic evolution of gapped spin systems , Phys. Rev. A 75
2007
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2010
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Sergey Bravyi, Matthew B. Hastings, and Spyridon Michalakis, Topological quantum order: Stability under local perturbations , J. Math. Phys. 51
2010
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Sergey Bravyi, Cristopher Moore, and Alexander Russell, Bounds on the quantum satisfiability threshold , ICS (Andrew Chi-Chih Yao, ed.), Tsinghua University Press, 2010, pp. 482–489
2010
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2010
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J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area laws for the entanglement entropy , Rev. Mod. Phys. 82
2010
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2010
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Stephen P. Jordan, David Gosset, and Peter J. Love, Quantum-Merlin-Arthur–complete problems for stoquastic Hamiltonians and Markov matrices , Phys. Rev. A 81
2010
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C. R. Laumann, A. M. Läuchli, R. Moessner, A. Scardicchio, and S. L. Sondhi, Product, generic, and random generic quantum satisfiability , Phys. Rev. A 81
2010
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C. R. Laumann, R. Moessner, A. Scardicchio, and S. L. Sondhi, Random quantum satisfiability , Quantum Inf. Comput. 10
2010
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2010
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Ramis Movassagh, Edward Farhi, Jeffrey Goldstone, Daniel Nagaj, Tobias J. Osborne, and Peter W. Shor, Unfrustrated qudit chains and their ground states , Phys. Rev. A 82
2010
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Bruno Nachtergaele, Benjamin Schlein, Robert Sims, Shannon Starr, and Valentin Zagrebnov, On the existence of the dynamics for anharmonic quantum oscillator systems , Rev. Math. Phys. 22
2010
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by same author, Lieb-Robinson bounds in quantum many-body physics , Entropy and the quantum, Contemp. Math., vol. 529, Amer. Math. Soc., Providence, RI, 2010, pp. 141–176. MR 2681770
2010
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Tobias J. Osborne, Jens Eisert, and Frank Verstraete, Holographic quantum states , Phys. Rev. Lett. 105
2010
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David Poulin, Lieb-Robinson bound and locality for general Markovian quantum dynamics , Phys. Rev. Lett. 104
2010
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Isabeau Prémont-Schwarz, Alioscia Hamma, Israel Klich, and Fotini Markopoulou-Kalamara, Lieb-robinson bounds for commutator-bounded operators , Phys. Rev. A 81
2010
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Isabeau Prémont-Schwarz and Jeff Hnybida, Lieb-robinson bounds on the speed of information propagation , Phys. Rev. A 81
2010
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Norbert Schuch and J. Ignacio Cirac, Matrix product state and mean-field solutions for one-dimensional systems can be found efficiently , Phys. Rev. A 82
2010
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by same author, Continuous matrix product states for quantum fields , Phys. Rev. Lett. 104
2010
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Tzu-Chieh Wei, Michele Mosca, and Ashwin Nayak, Interacting Boson Problems Can Be QMA Hard , Phys. Rev. Lett. 104
2010
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2011
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Daniel Gottesman, private communication , 2011
2011
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Ulrich Schollwöck, The density-matrix renormalization group in the age of matrix product states , Ann. Phys. 326
2011
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