I've been running VQE experiments locally using both the statevector_simulator and qasm_simulator, however I've noticed that the runtimes for the qasm_simulator are significantly longer than that of statevector_simulator. According to this answer the statevector_simulator produces ideal/deterministic results, whereas qasm_simulator produces non-ideal/probabilistic results. However I don't see why the simulation times should differ significantly($>\times 100$) if the number of shots=1 for the qasm_simulator even if a NoiseModel or measurement_error_mitigation_cls=CompleteMeasFitter is used.

Is this in fact expected and how is it explained?


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Note that if you use qasm_simulator with shots=1, this doesn't tell you anything! Unless IBM automatically switch your simulator to statevector_simulator if you specify the shots =1 when calling qasm_simulator.

Now in term of add noise model and doing measurement_error_mitigation. To be able to do this, you need to generate $2^n$ basis states and measure each of them to create a calibration matrix. It is an expensive procedure since you have many more quantum circuits to execute. Each circuit requires a certain amount of shots, up to 8192 shots. In statevector_simulator, you don't need to do this as there is no noise.


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