  In recent years, Variational Quantum Algorithms (VQAs) have emerged as a
promising approach for solving optimization problems on quantum computers in
the NISQ era. However, one limitation of VQAs is their reliance on
fixed-structure circuits, which may not be taylored for specific problems or
hardware configurations. A leading strategy to address this issue are
Adaptative VQAs, which dynamically modify the circuit structure by adding and
removing gates, and optimize their parameters during the training. Several
Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement
capability and hardware compatibility, have already been proposed in the
literature, but there is still lack of a systematic comparison between the
different methods. In this paper, we aim to fill this gap by analyzing three
Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable
Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE
(RA-VQE), a random approach we introduce as a baseline. In order to compare
these algorithms to traditional VQAs, we also include the Quantum Approximate
Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to
QUBO problems and study their performance by examining the quality of the
solutions found and the computational times required. Additionally, we
investigate how the choice of the hyperparameters can impact the overall
performance of the algorithms, highlighting the importance of selecting an
appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks
for Adaptative VQAs designed for near-term quantum devices and provides
valuable insights to guide future research in this area.
