  Variational Quantum optimization algorithms, such as the Variational Quantum
Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are
among the most studied quantum algorithms. In our work, we evaluate and improve
an algorithm based on VQE, which uses exponentially fewer qubits compared to
the QAOA. We highlight the numerical instabilities generated by encoding the
problem into the variational ansatz and propose a classical optimization
procedure to find the ground-state of the ansatz in less iterations with a
better or similar objective. Furthermore, we compare classical optimizers for
this variational ansatz on quadratic unconstrained binary optimization and
graph partitioning problems.
