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The Bose-Hubbard Model is QMA-complete

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Figure 1.1: We design graphs for two-qubit gates with overlapping regions as shown in (1 and 2 are associated with the first encoded qubit and regions 3 and 4 are associated with the secondA)
Figure 1.2: Each choice for the coefficients thop and Jint defines a computational problem
Figure 5.1: The graph g0.
Figure 5.2: Diagram elements from which a gate diagram is constructed. Each diagram element is aschematic representation of the graph g0 shown in Figure 5.1.
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The boundary gadget The gate graph The occupancy constraints graph Configurations Soundness Matrix elements of H out

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