Resource reduction for variational quantum algorithms by non-demolition measurements

We present a comparative study of two implementations of a variational quantum algorithm aimed at minimizing the energy of a complex quantum system. In one implementation, we extract the information of the energy gradient by projective measurements. In the second implementation, called the Non-Demolition approach, the gradient information is stored in a quantum detector, which is eventually measured. As prototypical examples, we study the energy minimization of the Lithium-based molecules and then extend the analysis systems with increased complexity. We find that, while both approaches are able to identify the energy minimum, the Non-Demolition approach has a clear advantage in terms of the overall computational resources needed. This advantage increases linearly with the complexity of the quantum system, making the Non-Demolition approach the ideal candidate to implement such variational quantum algorithms.