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Quantum advantage/supremacy was achieved by Google using a quantum computer and more recently by Pan Jianwei's group using photons. So I was wondering, has any analog quantum simulator showed quantum advantage yet? If yes, which one? And if not, what are the biggest hurdles?

If I'm not mistaken, current quantum simulators are in the range of hundreds of qubits, and thus they are already big enough to be difficult to simulate classically. Furthermore, even though they cannot perform universal computation, they are well suited to perform Hamiltonian simulation, at least for certain Hamiltonians.

Are these devices capable of simulating classically intractable Hamiltonians? If not, are they expected to be capable soon?

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