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The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters.
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Nondeterministic exponential time has two-prover interactive protocols
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Raussendorf, R. & Briegel, H. J · 2001
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Fault-tolerant quantum computation by anyons
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Efficient classical simulation of slightly entangled quantum computations
Vidal, G · 2003
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Renormalization algorithms for quantum-many body systems in two and higher dimensions
Verstraete, F. & Cirac, J. I · 2004
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The density-matrix renormalization group
Schollwöck, U · 2005
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Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
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Criticality, the area law, and the computational power of projected entangled pair states
Verstraete, F., Wolf, M. M., Perez-Garcia, D. & Cirac, J. I · 2006
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Entanglement renormalization
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Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
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Simulation of quantum many-body systems with strings of operators and monte carlo tensor contractions
Schuch, N., Wolf, M. M., Verstraete, F. & Cirac, J. I · 2008
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Infinite time-evolving block decimation algorithm beyond unitary evolution
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Computational complexity: a modern approach (Cambridge University Press, 2009)
Volume-law scaling for the entanglement entropy in spin-1/2 chains
Vitagliano, G., Riera, A. & Latorre, J · 2010
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The density-matrix renormalization group in the age of matrix product states
Schollwöck, U · 2011
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Quantum simulation of time-dependent hamiltonians and the convenient illusion of hilbert space
Poulin, D., Qarry, A., Somma, R. & Verstraete, F · 2011
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
Orús, R · 2014
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Deep learning
LeCun, Y., Bengio, Y. & Hinton, G · 2015
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Berry, D. W., Childs, A. M., Cleve, R., Kothari, R. & Somma, R. D · 2015
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Universal blind quantum computation
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