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A family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family.
Casimir invariants and vector operators in simple and classical Lie algebras
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The complexity of satisfiability problems
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Rigorous results on valence-bond ground states in antiferromagnets
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Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
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Nonlocal parameters for multiparticle density matrices
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Boolean constraint satisfaction: complexity results for optimization problems with arbitrary weights
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Complexity Classifications of Boolean Constraint Satisfaction Problems
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Quadrupolar order in isotropic Heisenberg models with biquadratic interaction
K. Harada and N. Kawashima · 2002
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Classical and Quantum Computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
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Symmetries, Lie algebras and representations: A graduate course for physicists
J. Fuchs and C. Schweigert · 2003
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Merlin-Arthur games and stoquastic complexity, 2006
S. Bravyi, A. Bessen, and B. Terhal · 2006
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The complexity of the local Hamiltonian problem
J. Kempe, A. Kitaev, and O. Regev · 2006
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Quadrupolar phases of the s = 1 s=1 bilinear-biquadratic Heisenberg model on the triangular lattice
A. Läuchli, F. Mila, and K. Penc · 2006
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Perturbative gadgets at arbitrary orders
S. Jordan and E. Farhi · 2008
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The complexity of quantum spin systems on a two-dimensional square lattice
The local hamiltonian problem on a line with eight states is QMA-complete
S. Hallgren, D. Nagaj, and S. Narayanaswami · 2013
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A. Bookatz · 2014
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I. Georgescu, S. Ashhab, and F. Nori · 2014
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Perturbative gadgets without strong interactions
Y. Cao and D. Nagaj · 2015
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Quantum Hamiltonian complexity
S. Gharibian, Y. Huang, Z. Landau, and S. W. Shin · 2015
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R. Oliveira and B. Terhal · 2008
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The power of quantum systems on a line
D. Aharonov, D. Gottesman, S. Irani, and J. Kempe · 2009
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S U ( N ) SU(N) Heisenberg model on the square lattice: A continuous-N quantum Monte Carlo study
K. Beach, F. Alet, M. Mambrini, and S. Capponi · 2009
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Antiferromagnetic to valence-bond-solid transitions in two-dimensional S U ( N ) SU(N) Heisenberg models with multispin interactions
J. Lou, A.W. Sandwik, and N. Kawashima · 2009
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N. Schuch and F. Verstraete · 2009
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An Introduction to Quantum Spin Systems
J. Parkinson and D. Farnell · 2010
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Schrieffer–Wolff transformation for quantum many-body systems
S. Bravyi, D. DiVincenzo, and D. Loss · 2011
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The complexity of translationally-invariant spin chains with low local dimension, 2016
J. Bausch, T. Cubitt, and M. Ozols · 2016
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Complexity classification of local Hamiltonian problems
T. Cubitt and A. Montanaro · 2016
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Simple universal models capture all classical spin physics
G. De las Cuevas and T. Cubitt · 2016
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The complexity of finite-valued CSPs
J. Thapper and S. Živný · 2016
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The complexity of translationally-invariant low-dimensional spin lattices in 3D, 2017
J. Bausch and S. Piddock · 2017
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On complexity of the quantum Ising model
S. Bravyi and M. Hastings · 2017
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Efficient optimization of perturbative gadgets, 2017
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Universal quantum Hamiltonians, 2017
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The complexity of antiferromagnetic interactions and 2D lattices
S. Piddock and A. Montanaro · 2017
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