Aligning quantum kernels for detecting false data injection attacks in power systems

False Data Injection Attacks (FDIAs) are an elusive and impactful security threat in power systems. Existing solutions, such as those based on machine learning methods with classical kernels, suffer from weak noise resistance, extensive parameter tuning, and unstable performance in high-dimensional spaces. This work provides a novel solution to this problem from the perspective of quantum computing, specifically through the use of quantum kernel embedding (QKE). Classical kernels require costly hyperparameter searches that scale poorly with the number of measurements and often fail to separate sparse, overlapping attack patterns inherent in FDIA detection; by contrast, quantum kernel embedding leverages the exponentially large Hilbert space via shallow, fixed-depth circuits to generate highly expressive feature maps with far fewer tunable parameters, enabling more efficient and robust discrimination of subtle false-data-injection patterns. A kernel-alignment framework with a weighted loss function is proposed to tune the quantum circuit parameters so that the quantum kernel captures the imbalanced label structure and more effectively distinguishes attacked from normal data. Additionally, the Nyström approximation is extended to the quantum Hilbert space, utilizing only a subset of training data instead of the entire dataset, which enhances the scalability and computational efficiency of the method. Case studies on test systems and high-performance quantum simulators demonstrate the effectiveness of the method and evaluate its robustness under varying quantum incoherent noise.