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.
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.
Training deep neural networks is often hindered by the fragility of gradient-based methods, which suffer from vanishing or exploding gradients, sensitivity to initialization, and entrapment in poor local minima. In response to these shortcomings, we introduce a new gradient-free algorithm called Quantum-Inspired Adaptive Superposition Optimization (QIASO), which views weight learning as a probabilistic superposition of candidate solutions, a fundamentally new optimization approach. In contrast to being dedicated to a single weight ensemble, QIASO maintains a distribution over several candidates, which are amplified and suppressed according to dynamically changing weights assigned to them. The variational formulation of the amplitude evolution leads to a KL-regularized formulation of their evolution, which generalizes statistical physics, information geometry, and online optimization viewpoints. To prevent invalid convergence, QIASO incorporates a stochastic perturbation operator based on quantum tunnelling into the optimizer, enabling the optimization process to overcome local minima on the loss surface and converge to the optimal solution. We provide theoretical bounds, monotone convergence of loss reduction, and almost-sure convergence to local optima with mild assumptions. Complexity analysis via empirical techniques suggests that QIASO scales more efficiently than Grover-based quantum-inspired algorithms and incurs no overhead in gradient computation compared to ADAM. The overall findings indicated that QIASO is a viable option for neural training, particularly when combined with other paradigms that utilise either large-scale or gradient-free approaches.
Adaptive quantum machine learning (QML) represents an exciting frontier at the intersection of quantum computing and classical bio-inspired optimization. The constraints of noisy intermediate-scale quantum (NISQ) devices—limited qubit counts, significant decoherence, and measurement uncertainties—pose formidable challenges to training parameterized quantum circuits (PQCs) using traditional gradient-based methods. To overcome these hurdles, we propose a novel Adaptive PSO–QML framework that integrates a particle swarm optimization (PSO)–inspired algorithm with dynamic hyperparameter adjustment, enabling real-time tuning of PQC parameters based on performance feedback. Unlike static optimizers, our approach continuously adapts its inertia weight and cognitive/social coefficients to balance exploration and exploitation, responding to stagnation or rapid improvement in measured fitness. We evaluate this hybrid algorithm on two benchmark classification tasks: the classical Iris dataset encoded into a 2-qubit circuit and a quantum-encoded subset of the MNIST dataset on 4 qubits. Our experiments, conducted on the Qiskit Aer simulator under realistic noise models (depolarizing, amplitude damping, and mixed), demonstrate that Adaptive PSO–QML achieves an average accuracy improvement of 12% over fixed-parameter PSO and 15% over Adam-based gradient descent, with p-values below 0.01 across paired t-tests. Statistical analysis summarized in Table 1 confirms the significance of these gains. Detailed simulation research further reveals that the adaptive mechanism not only accelerates convergence by approximately 30%—reducing total circuit evaluations—but also exhibits robust performance across varying circuit depths (1–3 entangling layers) and noise intensities. Our findings suggest that bio-inspired adaptation is a powerful tool for mitigating barren plateaus and noise effects in NISQ-era QML, paving the way for scalable quantum advantage in near-term hardware.
Training quantum neural networks (QNNs) on near-term hardware remains hampered by two compounding difficulties: the exponential vanishing of gradient variance known as the barren plateau, and the O(L⋅2n) time and memory cost of differentiating through an n-qubit, L-layer circuit. We propose RLQ-Grad, a reinforcement-learning-based optimizer in which a classical policy πφ (a spectrally-normalized PPO agent) learns to propose parameter updates directly, conditioned on the QNN's current parameters, loss, accuracy, and previous update. Because the surrogate gradient is emitted by a classical network rather than obtained by differentiating through the unitary U(θ), its variance is not constrained by the barren plateau concentration bound, and its cost scales with the number of trainable parameters rather than the Hilbert-space dimension. We prove these properties formally and verify them on a hardware-efficient ansatz across four supervised benchmarks with up to n=20 qubits. RLQ-Grad preserves a near-flat gradient-variance curve where backpropagation, parameter-shift, and adjoint differentiation decay by 1 to 2 orders of magnitude. Accounting for the full training pipeline (PPO rollouts, actor-critic updates, and optimizer states), RLQ-Grad needs under 2 MB of memory and runs 2490×, 7876×, and 673× faster per iteration than these three methods at n=20. It improves top-1 accuracy by up to +10% over gradient-based baselines on circuits of up to 12 qubits, and matches dedicated barren plateau mitigation methods on CIFAR-10 at 14 to 20 qubits, where evolutionary and gradient-free optimizers collapse to chance.
Optimisation of training still faces challenges due to an ill-conditioned loss surface and noisy gradient signals; at the same time, limited computational resources also restrict training options. Quantum Gradient Descent as a Hybrid Optimisation Strategy for Neural Network Training. The proposed noise-resilient quantum gradient descent framework maps selected gradient components to parameterised quantum circuits, estimates directional derivatives via parameter-shift measurements, and returns stable updates to the classical optimizer. It is not directly substituted for backpropagation; instead, it is a type of controllable gradient module that can be added to sensitive layers or low-dimensional projection heads. Add adaptive shot scheduling, damped momentum and layer-wise trust constraints to reduce estimator variance and prevent unstable quantum updates. Representative classification tasks are selected as the subjects of experiments for convergence speed, validation accuracy, gradient fidelity, measurement cost and noise robustness. Based on the above analysis, the new optimizer outperforms standard SGD in terms of final accuracy by 1.6% - 3.2% when using the same number of epochs; at the same time, it reduces the median gradient variance by 28.4% and maintains stable convergence even with an increase in simulated depolarizing noise from 0.001 to 0.015. Based on the above, it can be seen that Quantum Gradient Descent is not an all-purpose optimizer but rather a target-specific training accelerator for gradient-sensitive modules that can trade off sampling cost for more informative descent directions in measurement-aware update design.
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.
Deep learning's remarkable success hinges on iterative optimization algorithms like stochastic gradient descent (SGD). However, training deep neural networks often encounters challenges navigating highly non-convex loss landscapes, frequently leading to convergence issues, slow training speeds, and susceptibility to getting trapped in local minima. This paper introduces a novel optimization algorithm, Quantum-Inspired Adaptive Optimization (QIAO), drawing inspiration from quantum measurement processes—specifically probabilistic sampling and collapse models—to address these limitations. QIAO employs a probabilistic strategy to sample regions of the loss landscape and utilizes a collapse model to iteratively refine the search, effectively mimicking the behavior of quantum measurement. The core idea is to leverage the inherent uncertainty and probabilistic nature of quantum mechanics to guide the optimization process more effectively than traditional gradient-based methods. We propose a framework for QIAO that incorporates adaptive step size adjustments and a dynamically adjusted sampling strategy. We demonstrate the efficacy of QIAO through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to adapt to complex loss landscapes. This approach aims to provide a fundamentally different strategy for deep learning optimization, potentially offering improved convergence rates and robustness compared to conventional methods.