Callback function in VQD is defined but never used

[Anthony-Gandon]

What should we add?

The Variational Quantum Deflation algorithm has an attribute self._callback which is never used in vqd.solve().
Inspired by the code for the VQE algorithm, the callback should be called in the energy_evaluation() call.
It also seems interesting that the callback also informs the user of the current step (VQD runs k steps of VQE).

Currently, the test test_callback checks the equality of empty lists

history = {'eval_count': [], 'parameters': [], 'mean': [], 'std': []}

The change would consist in adding the following lines during the call of the energy_evaluation(). These lines were taken from the VQE algorithm.

if self._callback is not None:
    variance = np.real(expectation.compute_variance(sampled_expect_op))
    estimator_error = np.sqrt(variance / self.quantum_instance.run_config.shots)
    for i, param_set in enumerate(parameter_sets):
        self._eval_count += 1
        self._callback(self._eval_count, param_set, means[i], estimator_error[i], step)
else:
    self._eval_count += len(means)

Giving

history {
'eval_count': [1, 2, 3, 1, 2, 3],
'parameters': [array([ 3.61186007,  4.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ]), array([ 4.61186007,  4.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ]), array([ 4.61186007,  5.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ]), array([ 3.61186007,  4.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ]), array([ 4.61186007,  4.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ]), array([ 3.61186007,  5.19301252,  0.6019852 ,  5.94953681, -3.30704704,
        1.84629318, -5.4660436 ,  0.6984088 ])], 
'mean': [-1.0632369218371718, -1.4565924844031897, -1.360034418572368, 37.340083390662826,        48.54340751559681, 28.58589345125128], 
'std': [0.011432088966174363, 0.009556915198516208, 0.013956731222284432, 0.011432088966174363, 0.009556915198516208, 0.015443719747907501], 
'step': [1, 1, 1, 2, 2, 2]
}