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.
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.
Quantum machine learning is emerging as a new approach in the machine learning field that uses quantum properties, including superposition and entanglement. While the superposition offers low complexity when dealing with high-dimensional data, the entanglement has the potential to help us extract features better. Many classical and quantum optimizers have been proposed to train quantum machine learning models in the simulation environment. However, to the best of our knowledge, there is still no research investigating the best optimizer, which has the lowest resources and the minimal number of optimization steps, to achieve ideal performance. In this paper, we survey the most popular optimizers, such as Gradient Descent (GD), Adaptive Moment Estimation (Adam), and Quantum Natural Gradient Descent (QNG), through quantum compilation problems. We measure metrics that include the lowest cost value bound and wall time. We come to the conclusion that Adam is the most effective optimizer when achieving 1.94 times better in cost value and 1.10 times better in wall time at 9 qubits.
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.
This study presents a comprehensive comparison of multiple optimization algorithms applied to a quantum classification model, utilizing the Cleveland dataset. Specifically, the research focuses on three prominent optimizers—COBYLA, L-BFGS-B, and ADAM—each employing distinct methodologies and widely recognized in the domain of quantum machine learning. The performance of predictive models using these optimizers is rigorously evaluated through key metrics, including accuracy, precision, recall, and F1 score. The findings reveal that the COBYLA optimizer outperforms the L-BFGS-B and ADAM optimizers across all performance metrics, achieving an accuracy of 92%, precision of 89%, recall of 97%, and F1 score of 93%. Furthermore, the COBYLA optimizer exhibits superior computational efficiency, requiring only 1 min of training time compared to 6 min for L-BFGS-B and 10 min for ADAM. These results underscore the critical role played by optimizer selection in enhancing model performance and efficiency in quantum machine learning applications, offering valuable insights for practitioners in the field.
This study explores various architectures of Quantum Neural Networks (QNN) that utilize quantum computing to enhance machine learning model performance. The architectures examined include Hybrid Quantum Neural Network (H-QNN), Deep Quantum Neural Network (DQNN), Quantum Convolutional Neural Network (QCNN), and Coherent Feed Forward Quantum Neural Network. Additionally, the EfficientSU2 architecture demonstrated superior performance in accuracy and cost reduction. Optimization techniques such as Adaptive Moment Estimation (ADAM), Analytic Quantum Gradient Descent (AQGD), and Nakanishi-Fujii-Todo (NFT) were integrated to improve training efficiency. The study results show that EfficientSU2 with 10,000 iterations yielded the best results in terms of cost and accuracy across all tested datasets, with accuracy improvements reaching up to 97%. In conclusion, the EfficientSU2 architecture and the applied optimization techniques significantly enhanced the processing of complex data, paving the way for substantial advancements in quantum-based artificial intelligence applications.
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.
The efficient implementation of quantum computing is contingent upon high-fidelity quantum operations. Nevertheless, the fidelity of these operations is constrained by the precision of quantum system evolution control. The optimization of quantum control pulses is essential for improving the manipulation accuracy of superconducting qubits. Traditional optimization methods, including gradient descent and the gradient ascent pulse engineering algorithm, frequently encounter challenges such as slow convergence and susceptibility to local optima in pulse optimization problems. This study introduces an adaptive open-loop optimization algorithm based on the adaptive moment estimation (Adam) optimizer, capitalizing on the benefits of momentum and adaptive learning rate adjustments inherent in Adam. We conduct experimental analysis on the algorithm’s hyperparameters to achieve optimal solutions with a higher fidelity range at a faster convergence speed, effectively improving the fidelity and optimization efficiency of quantum gate operations. Through numerical simulations on the QuTiP platform, we validate the excellent performance of the Adam algorithm in quantum gate optimization. In optimizing the X and SWAP gates, its fidelity improved by 0.03% and 0.0016%, respectively, compared to the GRAPE algorithm. Compared to the CRAB method, the initial convergence speed of the Adam method increased fivefold, enabling it to achieve the target fidelity more rapidly. Future research will investigate closed-loop optimization strategies, utilizing feedback derived from the fidelity results of actual quantum computers to further augment quantum control performance