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.

近年来，变分量子算法（VQAs）作为在 NISQ 时代解决量子计算机上的优化问题的一种有前途的方法已经出现。然而，VQAs 的一个限制是它们对于特定问题或硬件配置可能不适合的固定结构电路。应对这个问题的一种主要策略是自适应 VQAs，通过添加和移除门来动态修改电路结构，并在训练过程中优化其参数。本文通过分析三种自适应 VQAs（进化变分量子特征求解器（EVQE），可变组态（VAns）和随机自适应 VQE（RA-VQE））来填补这一领域现有方法之间缺乏系统比较的空白。为了将这些算法与传统的 VQA 进行比较，我们还在分析中包括了量子近似优化算法（QAOA）。我们将这些算法应用于 QUBO 问题，并通过检查找到的解的质量和所需的计算时间来研究它们的性能。此外，我们还调查了超参数选择如何影响算法的整体性能，强调了选择适当的超参数调整方法的重要性。我们的分析为面向近期量子设备设计的自适应 VQAs 设定了基准，并为指导未来的研究提供了宝贵的见解。