Feature Encoding in Quantum Machine Learning: A Survey and Practical Guidelines

The efficient encoding of classical data into quantum states represents a significant performance bottleneck in Quantum Machine Learning (QML) applications on Noisy Intermediate-Scale Quantum (NISQ) devices. A notable gap exists in current research regarding a unified framework that jointly characterizes the resource cost, expressivity, and noise robustness of various feature encoding schemes, alongside providing actionable selection guidelines for practitioners. This project addresses this challenge through a systematic review and analysis of prominent feature encoding methodologies in QML. It establishes a three-axis taxonomy to classify major encoding families—such as basis, angle, dense-angle, amplitude, data re-uploading, and IQP encodings—based on independently measurable parameters of cost, expressivity, and robustness. The project further investigates

closed-form depth-fidelity bounds under NISQ decoherence channels, identifying critical gate-error rates that dictate the viability of specific encoding types. A unified treatment of Fourier expressivity, barren-plateau onset, and quantum kernel concentration is provided, offering a comprehensive trainability analysis as a function of the encoding circuit. The culmination is a five-regime decision framework designed to recommend hardware-grounded encoding strategies based on feature dimension, qubit budget, error rate, and task type, emphasizing the consistent preference for shallow angle-based encodings under specific error conditions.

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