Journal of the ACM (JACM)
The local Hamiltonian problem on a line with eight states is QMA-complete
Quantum Information & Computation
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We show that the quantum SAT problem is -complete when restricted to interactions between a three-dimensional particle and a five-dimensional particle. The best previously known result is for particles of dimensions 4 and 9. The main novel ingredient of our proof is a certain Hamiltonian construction named the Triangle Hamiltonian. It allows to verify the application of a 2-qubit CNOT gate without generating explicitly interactions between pairs of workspace qubits. We believe this construction may contribute to progress in other Hamiltonian-related problems as well as in adiabatic computation.