Janis AIAD

In this communication, we aim to present the solving of an MBDA’s use case related to optimal assignment, onto IBM online QPUs. The Quantum Approximate Optimization Algorithm (QAOA) (Farhi et al. 2014) is the base of our Variational Quantum Algorithm developed. We compare two methods to account for constraints, first primarily by integrating them into the Cost Hamiltonian with Lagrangian multipliers and second, by adapting the Mixer Hamiltonian according to (Wang et al. 2022) and (Fuchs et al. 2022). For the former, determining the optimal Lagrangian multipliers is generally a challenging task and the integration of constraints into the Cost Hamiltonian can significantly increase the associated circuit depth. The latter method aims to reduce the overall Hilbert space to only feasible solutions, which lets get rid of Lagrangian multipliers but may significantly enlarge the circuit associated to the Mixer Hamiltonian and make the initial state harder. It is then interesting to compare the circuit depth of both methods with respect to how well they are able to statistically put forward optimal solutions against non-optimal and non-feasible ones, still for relatively small sized instances, to fit on current QPUs.