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Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics. It mostly studies constraint satisfaction problems related to ground states of local Hamiltonians; that is, Hermitian matrices that act locally on a system of interest. The constraint satisfaction problems in quantum Hamiltonian complexity have led to the quantum version of the Cook–Levin theorem. Quantum Hamiltonian complexity has helped physicists understand the difficulty of simulating physical systems.
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