Abstract
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.
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Eldar, L., Regev, O. (2008). Quantum SAT for a Qutrit-Cinquit Pair Is QMA 1-Complete. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_72
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DOI: https://doi.org/10.1007/978-3-540-70575-8_72
Publisher Name: Springer, Berlin, Heidelberg
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