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I'm new to quantum annealing and D-Wave computer. I saw that it has about 5000 qubits which can solve a QUBO problem with 5000 variables.

From my understanding, if we use a gate model device, say, an IBM quantum device to solve a QUBO problem, the number of variables is equal to the number of qubits. Is that correct? If so, does it mean that DWAVE can solve larger scale problems than these gate model devices?

In terms of the resulting fidelity, which one is better? For example, if we want to solve maxcut problem, is it better to use the D-Wave machine or QAOA?

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This cannot yet be tested for more than about 100 qubits, since no publicly announced circuit-based quantum computer has been built with more than 127 qubits.

Furthermore, the word "efficiency" needs to be more precisely defined: Are we talking about speed, energy efficiency, number of total qubits needed, or something else? I'm glad that in your last paragraph you focused only on fidelity, which makes it much easier to answer your question, but still not easy. What precisely is meant by fidelity? You see, we can't just say "which device will give the answer with the best probability (i.e. the ground state with the highest fidelity)?" because it's possible that both devices eventually will get the correct ground state, but at different times. So the question then becomes a combination of fidelity-efficiency and time-efficiency and perhaps more.

If we use the same number of qubits (which is again like comparing apples and oranges because qubits for an annealing device aren't the same as qubits for a circuit-based quantum computing device), and allow the same amount of time, the D-Wave machine will likely give you the ground state of the QUBO problem faster than the circuit-based quantum computer regardless of what algorithm it uses (e.g. QAOA or something else) because D-Wave machines have been optimized for specifically that problem and only that problem.

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