Researchers at IQM France SAS and QbitSoft have demonstrated a performance gap between quantum and classical methods using a projected quantum kernel on quantum processors with 15, 30, and 45 qubits. The team achieved this on an engineered classification problem, with reproducible results across different quantum processing units.

The work also reveals that error mitigation techniques contribute unequally to performance gains, suggesting a subtle approach to error correction is important for realizing quantum speedup. This 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, the researchers state.

Engineered Quantum Kernel Classification for NISQ Devices

This outcome challenges the scarcity of demonstrable quantum speedup in machine learning, as researchers implemented a proposal for engineering classification tasks specifically designed to work with near-term, noisy intermediate-scale quantum (NISQ) devices. The team constructed an engineered learning problem using a function that generates training labels solely from training data, allowing for generalization to new, unseen test points and assessing the robustness of the quantum kernel’s predictive advantage.

These findings suggest a detailed relationship between noise, kernel fidelity and predictive performance, highlighting the importance of understanding how hardware limitations impact quantum machine learning algorithms. Error mitigation techniques did not contribute equally to widening the performance gap between quantum and classical approaches.

The researchers acknowledge the challenges of definitively proving quantum superiority, noting that correctness in some methods is inferred by extrapolating from quantum calculations possible with classical simulation, such as smaller system sizes or Clifford circuits. Despite the observed quantum advantage, the team faced limitations when comparing their results to classical matrix product state simulations, a benchmark that remains a primary challenge for demonstrating true quantum supremacy in machine learning.

Performance Gap with Projected Kernels up to 45 Qubits

This suggests that not all error mitigation strategies contribute equally to improving quantum machine learning outcomes. Analysis of the data showed that, for both projected quantum kernels, the performance gap increased with the amount of data used. These findings highlight the complex interplay between hardware fidelity, error mitigation and data availability in achieving demonstrable quantum advantage in machine learning tasks.

Scaling qubit counts did not dramatically alter the results.

Referee-Challenger Framework for Evaluating Quantum Performance

This experimental setup employed a “referee-challenger” framework, where data labels were assigned to maximize the performance difference between quantum and classical kernels, allowing for direct comparison of predictive accuracy. The researchers embedded data into quantum circuits to create the kernel, then retroactively assigned labels to amplify the distinction in performance between the quantum and classical approaches.

Data Embedding Strategy to Maximize Kernel Differentiation

The ability to differentiate kernel functions is directly linked to a model’s capacity for generalization, with a larger separation between the complexity of classical and quantum kernels potentially indicating superior quantum prediction performance. Researchers found that the complexity of the quantum model, defined by the quantum kernel, must be demonstrably lower than that of its classical counterpart to achieve a predictive advantage.

This difference in complexity dictates how well a model can perform on data it hasn’t seen before. The study quantified this separation to assess the potential for quantum machine learning to outperform classical methods.

Reproducibility Testing Across Different Quantum Processing Units

This cross-device testing ensured that any advantage wasn’t simply a result of tailoring labels to the noise profile of one particular machine. This approach allowed them to confirm that a performance difference wasn’t an artifact of fitting labels to the noise of a single device.

“Running the challenger on a different device from the referee tests cross-device reproducibility and ensures that a gap in accuracy between quantum and classical predictions is not caused by fitting labels to the noise of one device,” the paper states. This focus on reproducibility highlights the need for robust validation in quantum machine learning, moving beyond single-instance demonstrations towards more reliable and verifiable results.

These results confirm that even the largest experiments reported remain within the reach of current classical simulation methods, indicating that achieving a sustained quantum advantage requires designing quantum kernels specifically to inhibit leading simulation techniques.

Matrix Product State Simulation as a Benchmark for Quantum Advantage

Matrix product state simulations continue to present a significant hurdle for demonstrating definitive quantum advantage, even when quantum hardware exhibits superior empirical performance on specifically engineered problems. This simulation completed each circuit in under 20 seconds, with an error margin of 10^-2, revealing the persistent challenge of surpassing classical methods. The team’s analysis indicates that even with observed improvements in quantum hardware, classical simulations remain a critical benchmark for validation.

While techniques like Zero-Noise Extrapolation (ZNE) and Approximate Polynomial Transformation (APT) can open a gap in accuracy when used with engineered labels, only APT demonstrably improves the kernel itself. The researchers noted that ZNE did not enhance the accuracy of either hardware kernel when predicting ideal labels, highlighting the importance of correcting bias in the features used to construct the kernel.

The team’s work confirms that the classical difficulty of the engineered classification problem is a key component of achieving any observed quantum advantage. The ability of matrix product state simulations to closely match the quantum challenger’s performance emphasises that the data-encoding circuits remain classically simulable, even at larger qubit counts.

“As with any application relying on observables, beating classical simulation methods remains the primary challenge, as our matrix product state results here show,” the researchers state, emphasizing the need for increasingly complex and computationally demanding problems to truly showcase the potential of quantum machine learning.

The primary obstacle to achieving a sustained advantage, however, appears to be the development of circuit simulation techniques, necessitating close collaboration with the quantum simulation community to overcome these limitations and unlock the potential of quantum machine learning.

Source: https://arxiv.org/abs/2610.41848

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