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From official D-Wave docs:

The D-Wave 2000Q QPU has up to 2048 qubits and 6016 couplers.

For example, I have the optimization problem defined as the QUBO problem.

If I want to solve it on D-Wave, does it mean that my problem has to have at most 2048 variables (vertices) and no more than 6016 mutual dot products between variables (edges)?

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The vertices and edges are the number of qubits and connections in DWaves quantum processing unit topology. It is called Chimera Graph, see DWaves docs . The graph is not fully connected. Therefore an embedding of the qubo problem has to be done. It is done heuristically, see minorminer docs. As an example, if your problem is fully connected, the maximum number of variables in the qubo problem is currently 120 DWaveCliqueSampler.largest_clique. If you try to submit something bigger you get:

DWaveClique ValueError  :  Cannot embed given BQM (size 128), sampler can only handle problems of size 120

For sparse problems an embedding can be found for more than 120 variables. So it really depends on the problem structure.

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Yes for QUBO problems, vertices of the graph are qubits, and edges of the graphs are "couplers" which couple two qubits together.

For example for the QUBO problem:

$$\tag{1} b_1b_2 - 3b_1b_3 + b_3, $$

you need a machine with 3 qubits and 2 couplers (one between qubits 1 and 2, and one between qubits 1 and 3).

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