Despite quantum machine learning being an active topic of research, demonstrations of algorithms run on quantum hardware beating classical methods remain rare. In this work, we demonstrate a significant performance gap using a projected quantum kernel for $n=15,30$ and $45$ qubits over classical methods on an engineered classification problem, and show reproducibility of the results over different quantum processor units. We also demonstrate how error mitigation can widen this gap, both by improving hardware performance but also by increasing the classical difficulty, with different techniques contributing unequally to these phenomena. This work provides strong evidence that superior empirical performance of quantum hardware over all classical techniques is an achievable goal in quantum machine learning, albeit for an artificial problem. However, as with any application relying on observables, beating state-of-the-art simulation methods remains the primary challenge, as our matrix product state results here show.
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Can engineered quantum-kernel classification tasks retain a predictive-performance gap on noisy hardware, independently of device-specific noise? This paper implements projected quantum kernels using local Pauli expectations from Trotterized one-dimensional Heisenberg circuits on $15$, $30$ and $45$ superconducting qubits. Labels are engineered to separate quantum and classical kernels using a geometric-difference construction. Predictions are compared with eleven classical machine-learning baselines, with cross-validated hyperparameters and corrected resampled $t$-tests. Referee and challenger kernels use different devices at $15$ qubits and different same-device layouts at larger sizes.
Against the best circuit-agnostic classical baseline, the mean accuracy gap at $15$ qubits falls from $0.300$ at three Trotter steps to $0.040$ at ten steps, where it is no longer statistically significant. At $30$ and $45$ qubits, ten-step gaps remain $0.181$ and $0.170$. Zero-noise extrapolation and adaptive Pauli twirling restore significant gaps in the noisy $15$-qubit regime; readout mitigation does not. Comparisons against ideal kernels and swaps of mitigated referees/challengers distinguish changing the engineered task from improving prediction: extrapolation mainly changes labels, whereas adaptive twirling improves predictions on ideal labels.
These are not quantum-advantage results: bond-dimension-$128$ matrix-product-state simulation matches hardware prediction at $45$ qubits and ten steps, taking under $20$ seconds per circuit. Training-only label construction permits genuinely new test points but reduces gaps. Other limitations include artificial tasks, small datasets, overlapping larger-device layouts, and undisclosed details of adaptive Pauli twirling.
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Error found: The adaptive Pauli twirling results cannot be independently reproduced from this paper because the mitigation procedure is not specified and its details are deferred to a future publication.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Despite quantum machine learning being an active topic of research, demonstrations of algorithms run on quantum hardware beating classical methods remain rare. In this work, we demonstrate a significant performance gap using a projected quantum kernel for n=15,30 and 45 qubits over classical methods on an engineered classification problem, and show reproducibility of the results over different quantum processor units. We also demonstrate how error mitigation can widen this gap, both by improving hardware performance but also by increasing the classical difficulty, with different techniques contributing unequally to these phenomena. This work provides strong evidence that superior empirical performance of quantum hardware over all classical techniques is an achievable goal in quantum machine learning, albeit for an artificial problem. However, as with any application relying on observables, beating state-of-the-art simulation methods remains the primary challenge, as our matrix product state results here show.
Can engineered quantum-kernel classification tasks retain a predictive-performance gap on noisy hardware, independently of device-specific noise? This paper implements projected quantum kernels using local Pauli expectations from Trotterized one-dimensional Heisenberg circuits on 15, 30 and 45 superconducting qubits. Labels are engineered to separate quantum and classical kernels using a geometric-difference construction. Predictions are compared with eleven classical machine-learning baselines, with cross-validated hyperparameters and corrected resampled t-tests. Referee and challenger kernels use different devices at 15 qubits and different same-device layouts at larger sizes.
Against the best circuit-agnostic classical baseline, the mean accuracy gap at 15 qubits falls from 0.300 at three Trotter steps to 0.040 at ten steps, where it is no longer statistically significant. At 30 and 45 qubits, ten-step gaps remain 0.181 and 0.170. Zero-noise extrapolation and adaptive Pauli twirling restore significant gaps in the noisy 15-qubit regime; readout mitigation does not. Comparisons against ideal kernels and swaps of mitigated referees/challengers distinguish changing the engineered task from improving prediction: extrapolation mainly changes labels, whereas adaptive twirling improves predictions on ideal labels.
These are not quantum-advantage results: bond-dimension-128 matrix-product-state simulation matches hardware prediction at 45 qubits and ten steps, taking under 20 seconds per circuit. Training-only label construction permits genuinely new test points but reduces gaps. Other limitations include artificial tasks, small datasets, overlapping larger-device layouts, and undisclosed details of adaptive Pauli twirling.
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data outperforms fixed-measurement schemes followed by classical processing. It remained uncertain whether this performance gap persists at a finite scale, and in the presence of noise that is unavoidable with current quantum devices. In this work, we present simulations and analysis of the performance of existing hardware on a learning problem known to exhibit asymptotic advantage, now subjected to noisy quantum data. Comparing coherent quantum processing directly against fixed-measurement schemes, our results demonstrate a clear performance separation at a scale of just 30 to 40 noisy qubits. Already at this scale, the fundamental bottleneck is no longer classical computation but data acquisition; matching the noisy coherent protocol with measure-first strategies would still require months or even years of measurements. By systematically evaluating hardware constraints such as state preparation, gate errors, readout errors, connectivity, and coherence times, we provide evidence that a demonstration of such a strong learning advantage is accessible on near-term devices.
Quantum machine learning is considered one of the current research fields with great potential. In recent years, Havl\'{\i}\ifmmode \check{c}\else \v{c}\fi{}ek et al. [Nature (London) 567, 209 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced feature spaces, which effectively addressed a binary classification problem and offered a potential pathway to achieving quantum advantage. However, a straightforward binary classification algorithm falls short in solving multiclass classification problems. In this paper, we propose a quantum algorithm that rigorously demonstrates that quantum kernel methods enhance the efficiency of multiclass classification in real-world applications, providing quantum-enhanced performance. To demonstrate this, we design six distinct quantum kernels within the quantum algorithm to map input data into quantum state spaces and estimate the corresponding quantum kernel matrices. The results from quantum simulations reveal that the quantum algorithm outperforms its classical counterpart in handling six real-world multiclass classification problems. Furthermore, we leverage a variety of performance metrics to comprehensively evaluate the classification and generalization performance of the quantum algorithm. The results demonstrate that the quantum algorithm achieves superior classification and better generalization performance relative to classical counterparts.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs), constructed by embedding data into the Hilbert space of a quantum computer, are a particular quantum kernel technique that is particularly suitable for noisy intermediate-scale quantum devices. Unfortunately, kernel methods face three major problems: Constructing the kernel matrix has quadratic computational complexity in the number of training samples, choosing the right kernel function is nontrivial, and the effects of noise are unknown. In this work, we addressed the latter two. In particular, we introduced the notion of trainable QEKs, based on the idea of classical model optimization methods. To train the parameters of the QEK, we proposed the use of kernel-target alignment. We verified the feasibility of this method, and showed that for our experimental setup we could reduce the training error significantly. Furthermore, we investigated the effects of device and finite sampling noise, and we evaluated various mitigation techniques numerically on classical hardware. We took the best performing strategy and evaluated it on data from a real quantum processing unit. We found that using this mitigation strategy demonstrated an increased kernel matrix quality.
This work focuses on quantum machine learning and analyzes the power of one single qubit to solve classical machine learning problems. We explore possible strategies to address traditional supervised, unsupervised, and reinforcement learning tasks. In particular, we study binary and multinomial classification, regression problems, time series forecasting, clustering, and quantum reinforcement learning. Our results suggest that the same methodology could be used to address all three types of learning with different measurement strategies and, despite the strong limitation of reduced data dimensionality of the candidate problems, a single qubit can achieve similar or even improved performance with respect to state-of-the-art classic machine learning methods in many cases. As simulating the evolution of one qubit state is computationally efficient, our study enables the possibility to use the qubit model as a candidate solution to implement simple decision-making machine learning models in hardware with extremely low memory resources such as embedded systems or edge devices. The outcomes provided could be also of interest in academia and for the construction of demonstrators using low-scale contemporary quantum hardware.
Abstract The practical application of quantum machine learning algorithms, such as Quantum Neural Networks (QNNs), is currently constrained by their dependence on nascent, error-prone, and resource-intensive quantum hardware. This research introduces and validates a novel hybrid quantum- classical (HQC) algorithm engineered to deliver robust classification performance on modest, commodity classical hardware, thereby circumventing the quantum hardware bottleneck. Our multi-stage architecture strategically integrates advanced classical statistical analysis (Mahalanobis distance), a quantum-inspired kernel method (a hardened Quantum Support Vector Machine), and a quantum-inspired anomaly detection model (a Quantum Autoencoder). This ensemble was rigorously benchmarked on a synthetic dataset specifically engineered for extreme classification dinjculty (85-90%), characterized by high dimensionality, low informative features, and complex, multi- cluster class structures. The HQC algorithm achieved a notable weighted average accuracy of 42.66% across multiple experimental runs. This result is particularly significant when contextualized: it was achieved on a legacy classical server (Dell PowerEdge T110 II), yet it competitively approaches the performance envelope of state-of-the-art QNNs (55-70%) that require genuine quantum processors to exploit phenomena like superposition and entanglement. This work presents a compelling case for the strategic value of hybrid models as a pragmatic, resource- enjcient, and immediately deployable solution. It effectively bridges the gap between the theoretical promise of quantum computing and the practical demands of current computational ecosystems, offering a viable and powerful pathway toward the democratization of complex problem- solving