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- W2034763770 abstract "The calculation of ground-state energies of physical systems can be formalized as the $k$-local Hamiltonian problem, which is a natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more physically meaningful is to restrict the Hamiltonian in question by picking its terms from a fixed set $mathcal{S}$ and scaling them by arbitrary weights. Examples of such special cases are the Heisenberg and Ising models from condensed-matter physics. In this work we characterize the complexity of this problem for all 2-local qubit Hamiltonians. Depending on the subset $mathcal{S}$, the problem falls into one of the following categories: in $mathsf{ P}$; $mathsf{NP}$-complete; polynomial-time equivalent to the Ising model with transverse magnetic fields; or $mathsf{QMA}$-complete. The third of these classes has been shown to be $mathsf{StoqMA}$-complete by Bravyi and Hastings. The characterization holds even if $mathcal{S}$ does not contain any 1-local terms; for exa..." @default.
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- W2034763770 date "2016-01-01" @default.
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- W2034763770 title "Complexity Classification of Local Hamiltonian Problems" @default.
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- W2034763770 doi "https://doi.org/10.1137/140998287" @default.
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