Variational quantum classifiers (VQCs) are a leading approach for near-term quantum machine learning, but explaining their specific decisions remains a growing challenge. Classical ML has established tools for self-explanation, such as gradient-based heatmaps. However, quantum circuits trained on real hardware cannot use classical backpropagation, requiring quantum-native methods instead. This study applies one such method, the parameter-shift rule, to compute input gradients, resulting in saliency scores using two circuit evaluations per input feature. Using a small, controlled 2x2 image classification task with known ground-truth pixels, this study evaluates whether the model's explanations align with the features truly driving its predictions. The trained 4-qubit VQC achieves 100% test accuracy and identifies the correct causal pixels in 62.5% of test cases. To assess faithfulness more directly, ablation experiments show that masking saliency-identified pixels reduces model confidence by 3.97%, compared to 0.014% for random masking, a raw improvement of roughly 274x. Additional multi-seed analyses suggest the method remains reasonably consistent across different model initializations, helping show that explanation results are not from just one lucky training run. Overall, these results suggest that input parameter-shift saliency is a promising approach for Quantum explainability and motivate testing it on larger, more complex datasets.
Variational quantum classifiers (VQCs) are a leading approach for near-term quantum machine learning, but explaining their specific decisions remains a growing challenge. Classical ML has established tools for self-explanation, such as gradient-based heatmaps. However, quantum circuits trained on real hardware cannot use classical backpropagation, requiring quantum-native methods instead. This study applies one such method, the parameter-shift rule, to compute input gradients, resulting in saliency scores using two circuit evaluations per input feature. Using a small, controlled 2x2 image classification task with known ground-truth pixels, this study evaluates whether the model's explanations align with the features truly driving its predictions. The trained 4-qubit VQC achieves 100% test accuracy and identifies the correct causal pixels in 62.5% of test cases. To assess faithfulness more directly, ablation experiments show that masking saliency-identified pixels reduces model confidence by 3.97%, compared to 0.014% for random masking, a raw improvement of roughly 274x. Additional multi-seed analyses suggest the method remains reasonably consistent across different model initializations, helping show that explanation results are not from just one lucky training run. Overall, these results suggest that input parameter-shift saliency is a promising approach for Quantum explainability and motivate testing it on larger, more complex datasets.
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.
Abstract As machine learning grows increasingly complex due to big data and deep learning, model explainability has become essential to fostering user trust. Quantum machine learning (QML) has emerged as a promising field, leveraging quantum computing to enhance classical machine learning methods, particularly through quantum representation learning (QRL). QRL aims to provide more efficient and powerful machine learning capabilities on noisy intermediate-scale quantum (NISQ) devices. However, interpreting QRL models poses significant challenges due to the reliance on quantum gate-based parameterized circuits, which, while analogous to classical neural network layers, operate in the quantum domain. To address these challenges, we propose an explainable QRL framework combining a quantum autoencoder (QAE) with a variational quantum classifier (VQC) and incorporating theoretical and empirical explainability for image data. Our dual approach enhances model interpretability by integrating visual explanations via local interpretable model-agnostic explanations (LIME) and analytical insights using Shapley Additive Explanations (SHAP). These complementary methods provide a deeper understanding of the model’s decision-making process based on prediction outcomes. Experimental evaluations on simulators and superconducting quantum hardware validate the effectiveness of the proposed framework for classification tasks, underscoring the importance of explainable representation learning in advancing QML towards more transparent and reliable applications.
The practical value of quantum machine learning must be derived from efficiency rather than scale, as current NISQ processors support only small, shallow circuits. This paper evaluated whether variational quantum circuits (VQCs) can reduce the trainable parameter count in an image classification scenario while preserving accuracy. Experimentation compared quantum classifier heads to parameter-matched classical heads on an identical set of frozen features drawn from the Fashion-MNIST dataset by a CNN. 9 configurations of a quantum circuit crossed 4, 6, and 8 qubits with 1, 2, and 4 entangling layers, each matched to a multilayer perceptron with an approximately equal parameter count. The linear probes served as a floor baseline for all 105 runs across 5 random seed values. 7 out of 9 quantum-based configurations met the mean test accuracy of no more than 1 percentage point below its matched classical head, enforced by the pre-specified criterion. The 2 failures were single-layer circuits, with each falling roughly 8 points below its matched classical head and 12 points below the circuit-free linear probe; in total, 6 configs with 2+ layers passed, with the smallest at 74 trainable parameters. The general trend noticed was that accuracy increased progressively with depth. The 4-layer circuits exceeded the linear probe at every qubit count and produced the highest accuracy at 6 and 8 qubits. The simulation ran noiselessly; VQCs preserved accuracy at the matched parameter budget when depth was given, showcasing depth rather than qubit count gating performance.
Quantum Machine Learning (QML) is a newly emerging research area at the intersection of classical machine learning (CML) and quantum computing (QC). Data is becoming voluminous rapidly, so it is challenging for classical computers to train Machine Learning (ML) models over massive datasets. The hope is that quantum physics' intrinsic features, such as entanglement, superposition, and interference, could be exploited as resources for training ML models on big datasets that would otherwise be relatively impossible for classical computers. It is theoretically proven that quantum computers have an exponential-time advantage over their classical counterparts in solving several problems, e.g., complex large dimensional matrix multiplication, factorization problem, unstructured database search, etc. QML models attempt to find a quantum advantage over their classical counterparts. Variational Quantum Classifiers (VQC) are hybrid quantum neural networks to perform the task of classification using QML models. VQC models in the present NISQ (Noisy Intermediate Scale Quantum — 50 to 100 qubits) era can produce comparable and even better results than Classical models. In this article, we examined the performance of a VQC while performing a simple binary classification task. In this article, we use a VQC to evaluate this method's performance empirically. We constructed a VQC to predict the label of fresh input for the typical Iris dataset comprising pairings of target outputs and training inputs. Our quantum classifier can reasonably predict species labels using only four qubits. These levels are fairly good compared to the accuracy levels attained by classical classifiers.
Recent advancements in machine learning have revolutionised research across various fields. Despite their success, conventional learning techniques are hindered by their significant computational resources and energy requirements. Prompted by recent experimental breakthroughs in quantum computing, variational quantum machine learning (QML) – machine learning integrated with variational quantum circuits (VQCs) – has emerged as a promising alternative. Nonetheless, the theoretical framework underpinning the advantages of variational QML is still rudimentary. Specifically, the training of VQCs faces several challenges, such as the barren plateau problem, where the gradient diminishes exponentially with an increasing qubits. A related issue arises in variational QML training, where the convergence rate is exponentially small. In this thesis, we present theoretically guaranteed solutions to these challenges. First, we construct innovative circuit architectures to address the vanishing gradient problem in deep VQCs. We propose quantum controlled-layer and quantum ResNet structures, demonstrating that the expected gradient norm's lower bound is unaffected by the increase in qubits and circuit depth. Next, we introduce an initialization strategy to mitigate the vanishing gradient issue in general deep quantum circuits. We prove that Gaussian-initialized parameters ensure the gradient norm's decay rate remains inversely polynomial despite the increase in qubit numbers and circuit depth. Finally, we propose a novel and effective theory for analysing the training of quantum neural networks with moderate depths. We prove that, under certain randomness conditions in the circuits and datasets, training converges linearly with a rate inversely proportional to the dataset size. Our approach surpasses previous results, achieving exponentially larger convergence rates with modest depth, or conversely, requiring exponentially less depth for equivalent rates.
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.