This paper presents an empirical evaluation of the Qube Engine, a hybrid quantum-classical Variational Quantum Regressor (VQR) implemented on Noisy Intermediate-Scale Quantum (NISQ) systems. The framework integrates classical data encoding via single-qubit rotations, parameterized $RY+RZ$ variational layers, and linear entangling circuits evaluated on 4-qubit quantum registers. Optimization is conducted using classical algorithms (COBYLA) targeting Pauli-$Z$ expectation values and Mean Squared Error (MSE) loss on continuous feature spaces. We evaluate model performance across ideal statevector simulation (AerSimulator) and physical IBM Quantum superconducting processors (ibm_marrakesh, ibm_fez, ibm_kingston). Experimental results demonstrate consistent optimization dynamics and low simulation-to-hardware expectation drift ($\Delta = 0.0188$), corresponding to a 98.23% cross-backend output stability score under shallow circuit depths. This work provides a realistic analysis of variational regression dynamics, hardware execution variance, and structural trade-offs for near-term quantum machine learning models on NISQ hardware.
This paper presents an empirical evaluation of the Qube Engine, a hybrid quantum-classical Variational Quantum Regressor (VQR) implemented on Noisy Intermediate-Scale Quantum (NISQ) systems. The framework integrates classical data encoding via single-qubit rotations, parameterized RY+RZ variational layers, and linear entangling circuits evaluated on 4-qubit quantum registers. Optimization is conducted using classical algorithms (COBYLA) targeting Pauli-Z expectation values and Mean Squared Error (MSE) loss on continuous feature spaces. We evaluate model performance across ideal statevector simulation (AerSimulator) and physical IBM Quantum superconducting processors (ibm_marrakesh, ibm_fez, ibm_kingston). Experimental results demonstrate consistent optimization dynamics and low simulation-to-hardware expectation drift (Δ=0.0188), corresponding to a 98.23% cross-backend output stability score under shallow circuit depths. This work provides a realistic analysis of variational regression dynamics, hardware execution variance, and structural trade-offs for near-term quantum machine learning models on NISQ hardware.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
Quantum Support Vector Regression (QSVR) has emerged as one of the most promising quantum machine learning algorithms for nonlinear regression on Noisy Intermediate-Scale Quantum (NISQ) devices. However, despite numerous simulation-based studies, experimental evaluations on physical quantum hardware remain relatively scarce. This work presents a comparative analysis of three regression approaches: classical Support Vector Regression (SVR) with a Radial Basis Function (RBF) kernel, classical SVR utilizing precomputed quantum kernels, and the native QSVR implementation available in the qiskit-machine-learning framework. Experiments were conducted on three benchmark regression datasets using three execution environments: a noiseless Qiskit Aer simulator, the IQM Adonis hardware-aware simulator, and the physical 5-qubit IQM Spark superconducting quantum computer (Odra 5) located at Wrocław University of Science and Technology. Multiple quantum feature maps and circuit depths were investigated, while model hyperparameters were optimized using grid search. The obtained results demonstrate that QSVR can be successfully executed on contemporary superconducting quantum hardware and, for selected datasets, achieves prediction accuracy comparable to or exceeding that of a classical RBF-based SVR. The experiments further reveal the significant influence of quantum hardware noise, feature map selection, and circuit depth on regression quality. Moreover, the implementation based on precomputed quantum kernels generally exhibits greater robustness on physical hardware than the native QSVR implementation. The presented benchmark provides an experimental assessment of QSVR under realistic execution conditions and contributes to the ongoing evaluation of quantum machine learning algorithms on current NISQ-era quantum computers.
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.
With the advancement of quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid quantum-classical algorithms have emerged as promising approaches for addressing certain machine learning tasks. This study investigates the Variational Quantum Classifier (VQC), a hybrid model that integrates parameterized quantum circuits with classical optimization routines, implemented via IBM’s Qiskit framework. We provide a detailed account of the VQC architecture, including feature encoding, ansatz construction, and optimization methodology. To assess its performance, we conduct a comparative analysis between VQC and classical Support Vector Classifiers (SVC) across synthetic and real-world datasets, including Iris and a binary-filtered version of MNIST. Experimental results reveal that classical models consistently achieve higher accuracy and faster training times. However, the VQC demonstrates functional viability, particularly under noise-free conditions and reduced-dimensionality settings. These findings underscore the current limitations of quantum models while highlighting the potential of VQC as a proof-of-concept for quantum-enhanced learning as quantum hardware matures.
Quantum machine learning has emerged as a promising approach to enhance computational efficiency by leveraging the principles of quantum computing. However, the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, such as noise, limited qubit availability, and circuit depth constraints, restrict the implementation of fully quantum models. To address these challenges, this study focuses on the design, implementation, and performance evaluation of hybrid quantum-classical machine learning (HQML) models. The proposed approach integrates parameterized quantum circuits with classical optimization techniques to enable efficient learning within NISQ environments. The study employs standard benchmark datasets, including Iris, Breast Cancer, and MNIST, to evaluate the performance of the hybrid model. The results indicate that the HQML model achieves competitive accuracy on small and medium-sized datasets while maintaining balanced precision, recall, and F1-score. However, performance declines for complex datasets due to hardware limitations and noise effects. Additionally, the hybrid model demonstrates a lower number of parameters compared to classical deep learning models but requires higher training time due to iterative quantum-classical optimization. The findings highlight that hybrid quantum-classical models provide a practical and scalable approach for utilizing quantum computing in the current technological landscape. Although challenges related to noise, scalability, and computational overhead persist, advancements in quantum hardware and algorithm design are expected to improve performance. This study contributes to the growing field of quantum machine learning by providing a systematic framework for evaluating hybrid models on NISQ devices and identifying key areas for future research.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.