Hi @ankit27kh, thanks so much for your explanation! I agree that the resources for simulating a quantum computer on a classical computer are exponential and it would be unrealistic to simulate large quantum systems.
Recently I read this tutorial from Qiskit, which is about applying QAOA and VQE to solving portfolio optimization problems. A classical method is also provided as a benchmark model in this tutorial. Following this tutorial, I performed a set of experiments. When the number of assets is small (e.g. 4), it takes much longer time for QAOA to solve the problem than classical method. Then I increased the number of assets without changing other hyper-parameters and checked the running times of both QAOA and classical method. I found when the number of assets reaches about 25, QAOA starts to run faster than classical method. When the number is 29, QAOA can demonstrate about 3X speedup over classical method. It seems like QAOA has a polynomial time complexity while classical method has an exponential time complexity. All experiments were conducted in my local classical computer. So can we consider this speedup as a quantum advantage obtained from a quantum algorithm itself rather than the quantum simulator?
What I mean is as follows. Quantum simulators can not provide quantum advantage, due to the required exponential resources. But quantum algorithms, even implemented on classical computers, can still help achieve quantum advantage when solving certain problems.