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I've successfully run the $LiH$ VQE simulation detailed in Simulating Molecules using VQE using the statevector_simulator, however when attempting to run the same simulation on the quantum_instance(detailed in the same section) using the NoiseModel for ibmq_manhattan the simulation seems to run indefinitely without yielding results.

Is it expected that the quantum_instance simulation would be significantly longer ($>100\times$) than the statevector_simulator simulation?

Note: I'm using the following optimizer and variational form:

optimizer = SPSA(maxiter=100)
var_form = EfficientSU2(qubitOp.num_qubits, entanglement="linear")
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statevector simulator is a perfect/ideal simulation. It basically just manipulate the quantum state according to linear algebra. qasm_simulator with or without noise model is a shot based simulation that mimic the behavior of the device.

In other words, you can think of statevector simulator as performing a 1 shot experiment, whereas qasm_simulator is performing multiple shots simulation, hence it will take longer.

Note that as you go up in size, statevector simulation is not ideal... as you will run into memory problem... since you have to generate the entire Hamiltonian matrix and manipulate it. Whereas qasm simulator allows you to do this faster by not generating the entire Hamiltonian matrix.

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    $\begingroup$ I'm not sure that the last paragraph is correct. I'm not aware of any difference between the simulators in the generation of the Hamitonian. $\endgroup$ – Yael Ben-Haim Sep 28 '20 at 12:47

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