Efficiently navigating the high-dimensional laser fabrication parameter space for nanostructured TiO₂ sodium-ion pseudocapacitor electrodes is bottlenecked by the destructive, time-intensive nature of experimental data collection. We present an integrated predict–optimize–fabricate–validate engineering pipeline applied to a dataset of 5026 ULPING-fabricated electrodes, in which quantum kernel ridge regression (QKRR) and a variational quantum eigensolver (VQE) are rigorously benchmarked against well-tuned classical counterparts. At n = 200 training samples, QKRR and classical KRR show no practically meaningful difference in predictive accuracy (|ΔR²| < 0.002). At n = 50, however, QKRR fails on the capacitance retention and joint prediction tasks, yielding R² = −1.232 and −0.329 respectively, while classical KRR remains reliable; KRR is the preferred model at small sample sizes on this benchmark. On the optimization side, exhaustive grid search over the 480-point discrete fabrication space dominates VQE in both solution quality and wall-clock cost; the VQE results constitute a feasibility demonstration of running a quantum optimization loop on NISQ hardware, not evidence of optimizer-level advantage. A classical post-processing pipeline (kernel symmetrization, PSD projection, diagonal re-normalization) recovers simulator-level accuracy from raw IBM quantum hardware measurements (R² rising from 0.416 to 0.949 on the joint target at zero additional QPU cost). Importantly, generalization to genuinely novel laser fabrication conditions is limited: group-aware evaluation that holds out entire laser-parameter tuples yields R² in the range −0.7 to +0.4, indicating that reported in-distribution R² values reflect interpolation rather than extrapolation capability. Surrogate-optimized electrodes were experimentally fabricated and electrochemically validated, providing physical grounding for the pipeline independent of any quantum advantage claim.
Efficiently navigating the high-dimensional laser fabrication parameter space for nanostructured TiO₂ sodium-ion pseudocapacitor electrodes is bottlenecked by the destructive, time-intensive nature of experimental data collection. We present an integrated predict–optimize–fabricate–validate engineering pipeline applied to a dataset of 5026 ULPING-fabricated electrodes, in which quantum kernel ridge regression (QKRR) and a variational quantum eigensolver (VQE) are rigorously benchmarked against well-tuned classical counterparts. At n = 200 training samples, QKRR and classical KRR show no practically meaningful difference in predictive accuracy (|ΔR²| < 0.002). At n = 50, however, QKRR fails on the capacitance retention and joint prediction tasks, yielding R² = −1.232 and −0.329 respectively, while classical KRR remains reliable; KRR is the preferred model at small sample sizes on this benchmark. On the optimization side, exhaustive grid search over the 480-point discrete fabrication space dominates VQE in both solution quality and wall-clock cost; the VQE results constitute a feasibility demonstration of running a quantum optimization loop on NISQ hardware, not evidence of optimizer-level advantage. A classical post-processing pipeline (kernel symmetrization, PSD projection, diagonal re-normalization) recovers simulator-level accuracy from raw IBM quantum hardware measurements (R² rising from 0.416 to 0.949 on the joint target at zero additional QPU cost). Importantly, generalization to genuinely novel laser fabrication conditions is limited: group-aware evaluation that holds out entire laser-parameter tuples yields R² in the range −0.7 to +0.4, indicating that reported in-distribution R² values reflect interpolation rather than extrapolation capability. Surrogate-optimized electrodes were experimentally fabricated and electrochemically validated, providing physical grounding for the pipeline independent of any quantum advantage claim.
Developing high-rate electrodes is essential for Na-ion pseudocapacitors, next-generation devices that bridge the performance gap between high-energy density batteries and high-power density capacitors at a fraction of the cost of Li-ion analogs. Ultra-short laser pulses for in-situ nanostructure generation (ULPING) enables one-step fabrication of 3D-architected TiO₂ electrodes that minimize solid electrolyte interface (SEI) formation, but mapping laser parameters to electrochemical lifetime remains a significant data-driven challenge, particularly under sparse experimental sampling conditions. This study evaluates quantum machine learning (QML) methods such as quantum support vector regression (QSVR), quantum kernel ridge regression (QKRR), and quantum neural networks (QNN) for electrode performance prediction under noisy intermediate-scale quantum (NISQ) era constraints, with classical machine learning as a benchmark. Using 5026 unique configurations (26 experimentally realized + 5000 synthetic generated with a Conditional Variational Autoencoder, CVAE), noiseless quantum simulation achieved R² = 0.900, compared to a classical kernel ridge regression benchmark of R² = 0.9919. Introducing realistic device noise reduced performance substantially (≈60% with mitigation; ≈24% without). Real hardware experiments on IBM Quebec using four features and a 25/10 train-test split yielded R² = 0.150 for QSVR versus R² = 0.844 for classical SVR. However, mitigation strategies showed promise: zero-noise extrapolation improved quantum performance to R² = 0.580 (+287%), while combined readout error mitigation and ZNE reached R² = 0.696 (+364%). These results demonstrate the feasibility of an end-to-end framework for QML prediction models on noisy quantum hardware, quantify resource-accuracy trade-offs, and highlight the calibrated mitigation and scaling conditions under which quantum kernel methods may complement classical approaches as quantum processors mature, laying a methodological foundation for quantum-assisted materials informatics.
Accurate prediction of lithium-ion battery capacity fade across temperature extremes is critical for energy storage reliability, yet classical machine learning methods face challenges with the small, nonlinear datasets typical of accelerated aging studies. Quantum machine learning offers a potential solution through enhanced feature representation, but demonstrations on real quantum hardware remain limited. Here we benchmark quantum kernel ridge regression (Q-KRR) against classical baselines for battery capacity-fade prediction—a representative small-data problem with nonlinear, physics-driven features. Using six physics-informed descriptors, Q-KRR on a noiseless simulator achieved R 2 = 0.739, an 8.7% relative improvement over classical kernel ridge regression (R 2 = 0.680). On IBM's 127-qubit superconducting processor, systematic circuit optimization and targeted readout mitigation yielded R 2 = 0.770, exceeding both the classical baseline (13% relative gain) and the ideal simulator performance (4% absolute gain). This hardware advantage resulted from reducing circuit depth and qubit count while applying selective error mitigation matched to the dominant noise sources. The results demonstrate that quantum kernels can outperform classical methods on current noisy hardware when algorithms are co-designed with device constraints, offering a practical pathway for quantum-enhanced prediction in materials science and engineering domains characterized by limited training data and structured feature spaces.
Objective: This study evaluated quantum optimization algorithms-specifically the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA)-as optimization tools within a Quality by Design (QbD) framework for pharmaceutical tablet formulation, benchmarking them against established classical optimizers: Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Bayesian optimization. Methods: Thirty-six metformin hydrochloride tablet formulations were prepared using a central composite design with three independent variables. QbD employed response surface methodology (RSM) to build predictive models for five critical quality attributes (CQAs). These RSM surrogate models then served as the shared objective function for all optimizers: VQE and QAOA (IBM Qiskit simulators), NSGA-II, and Bayesian optimization with expected hypervolume improvement (qEHVI). Optimization quality was assessed using experimental desirability scores from verification batches, prediction error at optimizer-selected points, root mean square error (RMSE), coefficient of determination (R²), paired t-tests, and Bland–Altman analysis. Results: RSM models showed excellent fit (adjusted R²: 0.9412–0.9847). QbD desirability function achieved 0.871, VQE 0.884, NSGA-II 0.879, and Bayesian optimization 0.876, with no statistically significant differences among optimizers (p>0.05). QbD demonstrated superior predictive precision for individual CQAs. Evaluation-budget-normalized analysis showed quantum methods required substantially more function evaluations than classical optimizers, indicating no practical quantum advantage at this problem dimensionality. Conclusion: Quantum optimization showed no measurable advantage over classical methods for this three-variable problem. QbD remains the standard for regulatory-compliant pharmaceutical development. The principal contribution is a hybrid QbD-quantum framework where quantum algorithms serve as optimization tools within a QbD-defined design space.
The contemporary manufacturing landscape is more complicated, data-heavy and more automated than ever before, producing enormous volumes of multi-modal sensor data, production logs and maintenance records. Predictive analytics within these environments becomes essential to achieve operational efficiency, reduce downtime, and optimise resource allocation; however, many classical machine learning methods struggle with high-dimensional, nonlinear, and dynamic data, resulting in suboptimal predictions and slow decision-making. To overcome these issues, the proposed research suggests a Quantum-Enhanced AI (QAI) system combining various quantum algorithms: Quantum Neural Networks (Quantum Neural Network) to recognize patterns, Quantum Supporter Vector Machines (Quantum Supporter Vector Machines) to classify, Quantum Approximate Optimization Algorithm (Quantum Approximate Optimization Algorithm) to schedule production and allocate resources, and Variational Quantum Eigensolver (Variational Quantum Eigensolver) to optimize parameters under noisy settings or conditions into a hybrid quantum-class The framework is a quantum computer based framework that encodes classical manufacturing data in the form of quantum states, using amplitude and qubit-efficient embeddings, allowing representation of high-dimensional features with the parallelism and entanglement of quantum computing. Realworld experimental validation of both turbofan engine degradation and semiconductor manufacturing sensor logs was conducted using IBM Qiskit and PennyLane to ensure reproducibility, with noise-aware training and error mitigation policies applied in simulations on NISQ-era hardware. The proposed QAI framework demonstrated higher predictive accuracy (12 to 15) than state-of-the-art hybrid quantum-classical and classical models, with superior accuracy, memorability, and F1 scores, and showed exceptional capabilities in anomaly detection, failure prediction, and optimisation. The results validate that quantum algorithms can be integrated into a predictive analytics pipeline to overcome classical computation bottlenecks, enhance robustness, and provide actionable insights for making real-time manufacturing decisions. Overall, this paper has demonstrated that quantum-assisted AI can be beneficial in intelligent manufacturing environments, laying the groundwork for expanding practical applications that bridge the gap between the promises of quantum computational power and predictive analytics in the industry.
Abstract—Quantum Machine Learning (QML) operating on Noisy Intermediate-Scale Quantum (NISQ) hardware represents an emerging computational paradigm to address high-dimensional optimization problems that challenge classical Von Neumann supercomputing architectures. By mapping complex feature vectors into exponentially large 2^N Hilbert state spaces via Parameterized Quantum Circuits (PQCs) and Variational Quantum Algorithms (VQAs), QML targets computational advantages in combinatorial optimization, high-dimensional classification, and quantum-enhanced molecular modeling. However, the theoretical promise of NISQ-era variational computing is severely constrained by three fundamental bottlenecks: (1) Barren Plateaus, characterized by the exponential concentration of measure and vanishing variance of cost function gradients; (2) Hardware Decoherece Noise and readout error rates that corrupt quantum state fidelity; and (3) Classical-to-Quantum State Preparation bottlenecks that can erase theoretical computational speedups. This paper delivers an exhaustive, mathematically formal technical investigation and empirical benchmark of QML architectures for high-dimensional optimization. We formalize the Haar-distributed geometric mechanics of barren plateaus under 2-design unitary assumptions, evaluate barren plateau mitigation through shallow local cost operators and layer-by-layer parameter initialization, and contrast Variational Quantum Eigensolvers (VQE) with Quantum Kernel Support Vector Machines (Q-SVM). Furthermore, we construct an empirical benchmarking testbed executing across both state-vector simulators and superconducting quantum backends (IBM Quantum Heron / Eagle architectures), evaluating 127-qubit Hamiltonian optimization and high-dimensional financial portfolio allocation. Our findings demonstrate that while global cost functions suffer exponential gradient decay Var[grad] ~ O(2^-N) across circuit depth d >= 4, local Hamiltonian decomposition maintains trainable variance, achieving a 98.2% ground-state fidelity under zero-noise extrapolation (ZNE) error mitigation. Finally, we formulate open challenges in quantum error mitigation scaling, non-perturbative barren plateau escapes, and quantum data loading efficiency. Index Terms—Quantum Machine Learning (QML), Parameterized Quantum Circuits (PQCs), Variational Quantum Eigensolver (VQE), Barren Plateaus, Quantum Kernel Methods, NISQ Computing, Error Mitigation, Hilbert Space.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.