Previously, quantum kernel estimation required a significant number of measurement shots, limiting the scale of quantum machine learning tasks. Jian Xu and colleagues at the University of Science and Technology of China created AQKA (Active Quantum Kernel Acquisition). This is a new way to allocate these shots that intelligently distributes them based on each entry’s contribution to the downstream classifier. AQKA is a new technique for efficient use of measurement resources in quantum kernel learning. It’s a field that uses quantum computers to analyze data, similar to how traditional machine learning algorithms work, but potentially faster for certain problems. Quantum kernel learning aims to map classical data to a high-dimensional quantum feature space. In this space, machine learning algorithms can more easily identify patterns. The computational intensity arises from the need to estimate a kernel matrix that represents the similarity between data points in this quantum space. This estimation traditionally requires running many quantum circuits to collect enough statistical data.
Unlike existing methods that evenly distribute shots within a selected subset of data, this method intelligently allocates resources by considering the impact of each entry on the final classification result. Demonstrations on IBM quantum hardware have shown that using AQKA can improve performance by up to 32 percent, establishing it as an important approach when resources are limited. AQKA improves performance by intelligently considering the contribution of each data point to the final classification result. Demonstrations on IBM quantum hardware revealed up to 32 percentage point improvements with AQKA, achieved through a decision tree-like process that selects the best approach based on available resources and the task at hand, especially when resources are limited. This adaptive strategy allows AQKA to outperform uniform sampling techniques, especially in scenarios where the number of available shots is significantly smaller than the size of the kernel matrix, a common limitation of short-term quantum devices.
AQKA demonstrates superior performance and efficient shot allocation of scalable quantum kernels
\texttt{ibm_pittsburgh} Performance improvements of up to +32 points on hardware kernels demonstrate AQKA’s superiority over existing quantum kernel learning methods on limited budgets. Estimating the quantum kernel typically involves 
N is the number of data points and S is the number of shots per entry, which is hindering near-term quantum device progress. Previously, scaling quantum machine learning tasks was severely limited by this bottleneck. Computational costs increase quadratically with the number of data points, making it difficult to apply quantum kernel techniques to large datasets. AQKA addresses this problem by reducing the number of shots required to achieve a comparable level of accuracy, thereby enabling processing of larger datasets with limited quantum resources.
The development of AQKA introduces regime decomposition to identify optimal conditions for use with Nyström-QKE and ShoFaR, providing a customized approach to shot allocation based on specific computational needs. Nyström-QKE and ShoFaR are well-established subsampling techniques that reduce the number of estimated kernel entries, but typically allocate shots uniformly across the selected entries. AQKA complements these methods by optimizing the allocation within the selected subset, further increasing efficiency. Tests on the \texttt{ibm_pittsburgh} quantum computer yielded improvements of +26 to +32 points, and live online tests on the \texttt{ibm_aachen} and \texttt{ibm_berlin} hardware improved average performance by +17.0 ±4.8 points and +14.0 ±8.5 points, respectively, demonstrating adaptability beyond simulation. These results highlight the robustness of AQKA across different quantum hardware platforms and different levels of noise. However, these gains are currently limited to specific kernel ridge regression tasks, and it remains to be shown how well AQKA performs with more complex machine learning models and large real-world datasets. Future work will focus on extending AQKA to other machine learning algorithms and evaluating its performance on more difficult datasets.
Optimize quantum kernel classification with gradient proportional shot assignment
AQKA (Active Quantum Kernel Acquisition) fundamentally restructures the way measurement shots are used in quantum kernel learning. Intelligently prioritizes entries based on their impact on the final classification result, calculating each data point’s contribution to the overall result rather than distributing shots evenly. This prioritization is based on closed-form acquisition theory and determines the optimal number of shots for each entry proportional to the slope and kernel values, effectively concentrating resources where they matter most. The slope in this context represents the sensitivity of the classification result to changes in a kernel entry, and the kernel value indicates the overall importance of that entry. AQKA ensures that the most informative data points are measured with higher accuracy by allocating more shots to entries with higher slope and kernel values. Experiments were conducted on \texttt{ibm_pittsburgh} (156 qubit Heron), \texttt{ibm_aachen}, and \texttt{ibm_berlin} hardware and provided data validating the effectiveness of this approach. The use of multiple hardware platforms demonstrates the general applicability of the method and its resilience to variations in quantum device properties.
Adaptive quantum kernel learning balances performance with limited resources
AQKA is a new method designed to optimize the use of precious measurement shots in quantum kernel learning, a critical step toward practical quantum machine learning. Nyström-QKE remains the preferred choice where quantum resources are abundant, highlighting the field’s persistent tension between algorithmic sophistication and hardware limitations. Nevertheless, this approach offers significant advantages when measurement shots are limited, a common limitation of current quantum computers, increasing performance by up to 25 percent in certain scenarios. This trade-off between algorithmic complexity and resource requirements is a central challenge in short-term quantum algorithm development.
The method introduces a new way to allocate measurement “shots”, the fundamental unit of computation in quantum computers, within quantum kernel learning. Prioritizing the data points that receive these shots based on their impact on classification goes beyond simply dividing resources evenly. Establishing a regime decomposition is important and provides a guide for choosing the optimal allocation strategy depending on the specific problem and available hardware, allowing for more nuanced applications of this technique. This decomposition identifies the scenarios in which AQKA is most effective and provides a framework for selecting the optimal shot allocation strategy based on the characteristics of the dataset and the capabilities of the quantum hardware. The ability to adapt to different conditions is critical to maximizing the performance of quantum kernel learning in real-world applications.
AQKA is a new method that improves the efficiency of quantum kernel learning by strategically allocating measurement shots. This study demonstrates that prioritizing data points based on their impact on classification improves performance over uniform allocation when the number of shots is limited, with improvements of up to 25 percentage points observed. This adaptive approach was validated on quantum hardware such as \texttt{ibm_pittsburgh}, \texttt{ibm_aachen}, and \texttt{ibm_berlin}. The authors established a regime decomposition to guide the selection of optimal allocation strategies and provided a framework for balancing algorithmic sophistication and hardware constraints.
