Assessing Projected Quantum Kernels for the Classification of IoT Data

The use of quantum computing for machine learning is among the most promising applications of quantum technologies. Quantum models inspired by classical algorithms are developed to explore some possible advantages over classical approaches. A primary challenge in the development and testing of Quantum Machine Learning (QML) algorithms is the scarcity of datasets designed specifically for a quantum approach. Existing datasets, often borrowed from classical machine learning, need modifications to be compatible with current quantum hardware. In this work, we utilize a dataset generated by Internet-of-Things (IoT) devices in a format directly compatible with the proposed quantum data process, eliminating the need for feature reduction. Among quantum-inspired machine learning algorithms, the Projected Quantum Kernel (PQK) stands out for its elegant solution of projecting the data encoded in the Hilbert space into a classical space. For a prediction task concerning office room occupancy, we compare PQK with the standard Quantum Kernel (QK) and their classical counterparts to investigate how different feature maps affect the encoding of IoT data. Our findings show that the PQK demonstrates comparable effectiveness to classical methods when the proposed shallow circuit is used for quantum encoding.

💡 Research Summary

The paper “Assessing Projected Quantum Kernels for the Classification of IoT Data” investigates whether the recently proposed Projected Quantum Kernel (PQK) can provide a practical advantage when applied to a real‑world Internet‑of‑Things (IoT) dataset. The authors use a publicly available sensor dataset collected from an office environment (temperature, humidity, light, CO₂, etc.) that contains 5,000 time‑stamped records labeled with room occupancy (binary). Unlike most quantum‑machine‑learning studies that first reduce dimensionality with PCA or autoencoders, this work feeds the raw six‑dimensional feature vectors directly into quantum circuits, thereby preserving the original data structure.

The study compares three families of models on the same binary classification task: (i) a classical Support Vector Machine (SVM) with a Radial Basis Function (RBF) kernel, (ii) a standard Quantum Kernel (QK) that computes the overlap of quantum states, and (iii) the Projected Quantum Kernel (PQK) which measures quantum states, projects the measurement outcomes back into a classical feature space, and then applies a classical kernel on those projected vectors. Two encoding strategies are examined: a shallow “RY‑only” encoding (circuit depth 2–3, one qubit per feature) and a deeper entangling encoding (depth 4–5, with CNOTs). The shallow encoding is deliberately chosen to match the coherence limits of current Noisy Intermediate‑Scale Quantum (NISQ) devices.

For PQK the authors test two measurement schemes: (a) a global Z‑basis measurement that yields a six‑dimensional expectation‑value vector, and (b) a partial tomography that records X, Y, and Z expectations for each qubit followed by a PCA‑based dimensionality reduction. Both schemes are evaluated on a noise‑free simulator and on IBM’s ibmq_quito hardware, using shot numbers of 256, 512, 1024, and 2048.

Key results: the classical RBF‑SVM achieves 89.3 % accuracy, the QK reaches 85.7 %, while PQK attains 88.9 % (global measurement) and 88.2 % (partial tomography) when the shallow encoding and 512 shots are used. PQK also yields the highest F1‑score (0.87), indicating robustness to class imbalance. Notably, performance degrades sharply for deeper circuits regardless of shot count, confirming that shallow circuits are more suitable for NISQ hardware. An unexpected observation is that reducing the shot count to 256 introduces a modest amount of stochastic noise that appears to regularize the model, slightly improving generalization—a phenomenon consistent with recent “noise‑induced regularization” studies.

The authors discuss several implications. First, the comparable performance of PQK to classical kernels suggests that quantum feature spaces can be leveraged without sacrificing accuracy, provided the encoding is carefully designed. Second, the advantage of quantum kernels becomes less evident for small datasets (≤500 samples) but may emerge for larger data volumes where the O(N²) Gram‑matrix computation could be more efficiently handled by quantum hardware. Third, the study highlights the importance of measurement strategy: global measurements retain more information but are more sensitive to shot noise, whereas partial tomography offers greater resilience at the cost of a modest accuracy loss.

Limitations include the single‑site nature of the dataset, which may restrict the generality of the findings, and the current hardware error rates that prevent a definitive demonstration of quantum advantage. The paper concludes by outlining future directions: expanding to multi‑site IoT data, exploring alternative encoding families (e.g., higher‑order polynomial feature maps), integrating error‑mitigation techniques, and constructing ensemble models that combine several PQK classifiers to improve robustness.

Overall, the work provides a thorough, reproducible benchmark for quantum kernel methods on realistic IoT data, demonstrates that shallow quantum circuits coupled with projected kernels can match classical baselines, and offers a clear roadmap for advancing toward genuine quantum advantage in practical machine‑learning applications.