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.

翻译：近年来，变分量子算法（VQAs）已成为NISQ时代在量子计算机上解决优化问题的一种有前景的方法。然而，VQAs的一个局限性在于它们依赖固定结构的量子线路，这可能无法针对特定问题或硬件配置进行优化。解决这一问题的领先策略是自适应VQAs，这类算法通过动态添加和删除量子门来修改线路结构，并在训练过程中优化其参数。文献中已提出多种基于量子线路浅度、纠缠能力和硬件兼容性等启发式策略的自适应VQAs，但目前仍缺乏对不同方法的系统性比较。本文旨在通过分析三种自适应VQAs来填补这一空白：进化变分量子本征求解器（EVQE）、可变拟设（VAns）（两者均为文献中已有方法），以及随机自适应VQE（RA-VQE）（我们将其作为基线引入的随机方法）。为将这些算法与传统VQAs进行对比，我们还将量子近似优化算法（QAOA）纳入分析中。我们将这些算法应用于QUBO问题，并通过评估所求解的质量和所需计算时间来研究其性能。此外，我们探讨超参数选择对算法整体性能的影响，强调选择合适超参数调优方法的重要性。我们的分析为面向近时期量子器件的自适应VQAs设立了基准，并为指导该领域未来研究提供了宝贵的见解。