Resource reduction for variational quantum algorithms by non-demolition measurements

Abstract 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. Graphical abstract Schematic representation of the energy minimization process for the H2 and LiH molecules using direct measurement (DM) and quantum non-demolition measurement (QNDM) approaches. Both methods converge to the minimum energy with similar accuracy, but the QNDM approach requires significantly fewer quantum resources (up to 79% reduction in gate count for LiH), highlighting its efficiency for variational quantum algorithms