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I have a list of transpiled circuits that I run on Aer.get_backend('aer_simulator').

qobj = assemble([mapped_circuit.bind_parameters(dict(zip(all_qiskit_params, all_param_values[:, pp])))
                         for pp in range(n_reps)], backend=backend, shots=N_shots)
job = backend.run(qobj)
counts = job.result().get_counts()

Depending on the N_shots the runtime is slower; I am okay with it, but by looking more closely I found that what really takes a long time is the call of job.result(), which goes to less than 1 sec for N_shots = 1e4, 8 secs for N_shots = 1e5to over a minute for N_shots = 1e6.

Is this expected or there is a faster way?

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backend.run submits the job, but job.result will wait for the outcome. So if you run a more expensive calculations, like sampling more shots, you will see more time spent in job.result.

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