qiskit QAOA on Aer GPU giving errors

Question

I am trying to run Qiskit QAOA algorithm on using aer simulator and device GPU. But I am not sure how to give this backend in the QAOA algorithm structure.

Here is a code:

nqubits = 5
H = QuantumCircuit(nqubits)
start = time.time()

sim = AerSimulator(method='statevector')
sim_gpu = AerSimulator(method='statevector', device='GPU')

for i in range(nqubits):
    H.z(i)
    H_op = MatrixOp(Operator(H))
    new_H = transpile(H, backend=sim)

    qaoa = QAOA(optimizer= COBYLA(), reps=1, mixer=new_H,
            initial_point=np.array([1.0]),
            quantum_instance=sim)

    res = qaoa.compute_minimum_eigenvalue(H_op)

end = time.time()

print("time taken : ", end - start)

I get this error:

QiskitError: 'Circuit execution failed: ERROR: Failed to load circuits: Invalid parameterization: instruction param position out of range'

I tried running the code via estimators but I am unable to see any speed-up.

def cost_func(params, ansatz, hamiltonian, estimator):
    cost = estimator.run(ansatz, hamiltonian, parameter_values=params).result().values[0]
    return cost

# Problem to Hamiltonian operator
hamiltonian = SparsePauliOp.from_list([("IIIZZ", 1), ("IIZIZ", 1), ("IZIIZ", 1),("ZIIIZ", 1)])
# QAOA ansatz circuit
ansatz = QAOAAnsatz(hamiltonian, reps=8)
x0 = 2 * np.pi * np.random.rand(ansatz.num_parameters)

estimator = Estimator(
    backend_options={
          "method": "statevector"
    },
    run_options={"shots": 1e4},
)

estimator_gpu = Estimator(
    backend_options={
           "method": "statevector",
           "device": "GPU"
    },
    run_options={"shots": 1e4},
)

sampler = Sampler(run_options= {"method": "statevector"})

start = time.time()
res = minimize(cost_func, x0, args=(ansatz, hamiltonian, estimator), method="COBYLA")
end = time.time()

print("Time Taken CPU: ", end-start)

start_gpu = time.time()
res_gpu = minimize(cost_func, x0, args=(ansatz, hamiltonian, estimator_gpu), method="COBYLA")
end_gpu = time.time()

print("Time Taken GPU: ", end_gpu-start_gpu)

Time Taken CPU: 2.922945022583008 Time Taken GPU: 2.9809350967407227

What is it that I am doing wrong?