Abstract Hybrid quantum machine learning (QML) relies on quantum variational circuits (QVCs) trained together with classical components. While gradient-based training is standard, it is costly on near-term hardware and vulnerable to barren plateaus, motivating gradient-free alternatives. However, there is limited systematic evidence comparing gradient-free methods to strong gradient baselines under matched quantum-evaluation budgets. A benchmark of 15 gradient-based, gradient-free, and hybrid optimizers is conducted on four binary classification datasets and two three-qubit QVC architectures using a unified experimental protocol under a fixed per-step quantum-evaluation budget. Across tasks, Adam is the strongest gradient-based method. Among the purely gradient-free schemes, Asexual Reproduction Optimization is the strongest optimizer; tournament-selection and elite-pool genetic algorithms (GA-Tourn, GA-Elite) also frequently match the best gradient-based configurations. Among the hybrid schemes, Gradient Lexicase Selection with Adam (GLS- Adam ) performs comparably. In contrast, the two gradient-free methods big bang–big crunch and a cross-entropy method variant often fail to improve beyond chance. Additional sensitivity analyses show that circuit depth can change the preferred optimizer, whereas finite-shot sampling budget and post-training backend-specific noise do not materially change the main conclusions. Overall, gradient-based methods remain robust defaults for hybrid QML, while a small subset of gradient-free and hybrid approaches provides viable alternatives under realistic quantum-evaluation constraints.
Abstract Hybrid quantum machine learning (QML) relies on quantum variational circuits (QVCs) trained together with classical components. While gradient-based training is standard, it is costly on near-term hardware and vulnerable to barren plateaus, motivating gradient-free alternatives. However, there is limited systematic evidence comparing gradient-free methods to strong gradient baselines under matched quantum-evaluation budgets. A benchmark of 15 gradient-based, gradient-free, and hybrid optimizers is conducted on four binary classification datasets and two three-qubit QVC architectures using a unified experimental protocol under a fixed per-step quantum-evaluation budget. Across tasks, Adam is the strongest gradient-based method. Among the purely gradient-free schemes, Asexual Reproduction Optimization is the strongest optimizer; tournament-selection and elite-pool genetic algorithms (GA-Tourn, GA-Elite) also frequently match the best gradient-based configurations. Among the hybrid schemes, Gradient Lexicase Selection with Adam (GLS- Adam ) performs comparably. In contrast, the two gradient-free methods big bang–big crunch and a cross-entropy method variant often fail to improve beyond chance. Additional sensitivity analyses show that circuit depth can change the preferred optimizer, whereas finite-shot sampling budget and post-training backend-specific noise do not materially change the main conclusions. Overall, gradient-based methods remain robust defaults for hybrid QML, while a small subset of gradient-free and hybrid approaches provides viable alternatives under realistic quantum-evaluation constraints.
Training parameterized quantum circuits requires balancing optimization progress with limited evaluation budgets and the statistical uncertainty of near-term quantum hardware. We present a modular benchmarking framework that separates quantum search-direction estimation from classical parameter-update rules, allowing their interactions and sensitivities to be examined independently. We evaluate a suite of gradient-based, stochastic, and derivative-free optimizers across combinatorial optimization using the Quantum Approximate Optimization Algorithm (QAOA), supervised quantum machine learning using Iris classification and a quantum convolutional neural network (QCNN) for binary MNIST classification, and quantum chemistry using the variational quantum eigensolver (VQE) for molecular hydrogen. By separating objective evaluations from sample-circuit costs under finite-shot simulation and physical execution on a 156-qubit processor, we compare optimizer behavior across workloads with different parameter counts and measurement requirements. Four selected simulator and hardware case studies report terminal and best observed objectives separately, alongside post-training classifier accuracies. The comparisons include selected MaxCut and hydrogen trajectories and illustrate workload-dependent objective changes and evaluation costs, while the simulator benchmark compares both peak and mean performance across three seeds. The hardware runs do not establish an optimizer ranking or isolate a causal effect of device noise.
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new parameters at every optimization step. However, this process can be extremely challenging, due to the nature of navigating the exponentially scaling complex Hilbert space, barren plateaus, and the noise present in all foreseeable quantum hardware. Although a variety of optimization algorithms are employed in practice, there is often a lack of theoretical or empirical motivations for this choice. To this end we empirically evaluate the potential of many common gradient and gradient free optimizers on a variety of optimization tasks. These tasks include both classical and quantum data based optimization routines. Our evaluations were conducted in both noise free and noisy simulations. The large number of problems and optimizers evaluated yields strong empirical guidance for choosing optimizers for QVCs that is currently lacking.
Abstract Reliable radar-based classification of small unmanned aerial vehicles (UAVs, drones) is hampered by low signal-to-noise ratio (SNR), non-Gaussian clutter, and site-specific shifts. This motivates interest in Quantum Machine Learning (QML) as a potentially more noise-resilient alternative to classical methods, yet reproducible advantages over strong classical baselines remain unclear. This study presents a controlled, like-for-like comparison between feed-forward neural networks and pure QML models without a preceding classical dimensionality-reduction encoder. All models operate on the same binned Fourier features. The QML variants span two data encodings (angle, amplitude), two variational circuit families, and an optional Quantum Fourier Transform, and are trained either with Adam or the gradient-free Asexual Reproduction Optimization (ARO) under matched evaluation budgets.Across three regimes (noiseless, additive white Gaussian noise (AWGN), and colored AR(1) complex Gaussian noise (cAR(1)-GN)), QML achieves competitive accuracy with only tens of parameters and, in two settings (noiseless and AWGN), slightly exceeds the best classical baselines, although these differences are not statistically significant. Under temporally correlated cAR(1) Gaussian noise, the tuned classical network significantly outperforms the best QML configuration. Overall, QML provides parameter-efficient performance parity in two of three conditions but no definitive advantage. The results highlight a strong dependence on the noise regime and point to angle-encoded, ARO-trained circuits as the most promising QML candidates for noisy radar-based drone classification.
Training deep neural networks remains difficult due to vanishing gradients, non-convex loss surfaces, and hyperparameter sensitivity. These obstacles are compounded by quantum machine learning, where barren plateaus, circuit depth, and hardware noise restrict the applicability of gradient-based approaches. To overcome these drawbacks, this study presents adaptive Grover-driven parallel quantum optimization (AG-PQO), a hybrid, gradient-free scheme that leverages Grover's quadratic search speedup, along with adaptive loss-aware discretization and fidelity-based regularization. In contrast to more classical optimizers, such as Adam or evolutionary strategies (ES), which are either sensitive to the adequacy of the gradient update or exhibit poor scaling behavior, AG-PQO optimizes by performing Grover-accelerated candidate exploration across layers and reuses high-quality solutions in quantum memory caching. Testing indicates that AG-PQO yields higher accuracy, 2%–3% above Adam and ES, and faster convergence with less end-value loss than Adam, ES, and quantum feedforward-backpropagation (QFB). It is worth noting that AG-PQO remains stable at the simulated noise level of NISQ and has the potential to scale to near-term quantum processors.
Quantum Machine Learning is gaining traction by leveraging quantum advantage to outperform classical Machine Learning. Many classical and quantum optimizers have been proposed to train Parameterized Quantum Circuits in the simulation environment, achieving high accuracy and fast convergence speed. However, to the best of our knowledge, currently there is no related work investigating these optimizers on multiple algorithms, which may lead to the selection of suboptimal optimizers. In this paper, we first benchmark the most popular classical and quantum optimizers, such as Gradient Descent (GD), Adaptive Moment Estimation (Adam), and Quantum Natural Gradient Descent (QNG), through the Quantum Compilation algorithm. Evaluated metrics include the lowest cost value and the wall time. The results indicate that Adam outperforms other optimizers in terms of convergence speed, cost value, and stability. Furthermore, we conduct additional experiments on multiple algorithms with Adam variants, demonstrating that the choice of hyperparameters significantly impacts the optimizer's performance.
Abstract Distributed quantum machine learning (QML) provides a natural framework for studying variational quantum models under distributed and feature-partitioned execution, but the accuracy-practicality trade-offs of vertical partitioning in the near-term regime remain insufficiently quantified. This work presents a controlled benchmark of a centralized hybrid reference model against vertically distributed QML architectures that split input features across two variational quantum circuits and combine the resulting low-dimensional measurement outputs either through a trainable dense layer or through parameter-free quantum-only aggregation rules. The models are evaluated on four binary-classification datasets under both gradient-based Adam and gradient-free ARO (asexual reproduction optimization). To assess hardware transfer, simulator-trained models are executed on IBM superconducting quantum processors using fixed-weight inference. Across all datasets, the centralized hybrid model achieves the highest mean accuracy, whereas the distributed variants require substantially fewer trainable parameters (24 or 31 versus 300), revealing a clear accuracy-capacity trade-off. The results further show that optimizer choice is particularly important for quantum-only aggregation rules. Hardware experiments yield accuracies broadly consistent with simulator re-evaluation, while stronger runtime resilience settings improve stability at the cost of increased execution time.