🤖 AI Summary
This study addresses the lack of a unified evaluation framework for classical data encoding on noisy intermediate-scale quantum (NISQ) devices by systematically reviewing 66 core studies from 2017 to 2026 and proposing the first triaxial classification scheme based on cost, expressivity, and noise robustness. Leveraging quantum circuit complexity analysis, decoherence modeling, and Fourier spectral methods, the work derives a closed-form bound on circuit depth versus fidelity under NISQ constraints, unifying the characterization of Fourier expressivity, barren plateaus, and kernel concentration phenomena. A four-dimensional parameter-driven encoding recommendation mechanism is established, revealing that shallow-angle encoding outperforms amplitude encoding in practical settings when gate error rates satisfy $p \geq 10^{-3}$. These insights yield a hardware-aware strategy for optimal encoding selection.
📝 Abstract
The encoding of classical data into quantum states constitutes the primary performance bottleneck in Quantum Machine Learning (qml) on Noisy Intermediate-Scale Quantum (nisq) devices. No existing framework jointly characterises resource cost, expressivity, and noise robustness, nor provides actionable selection guidelines for practitioners. This survey addresses that gap through a systematic review of 66 primary works (2017-2026) assembled via a PRISMA-adapted protocol across five academic databases. Four principal contributions are made. First, a three-axis cost-expressivity-robustness taxonomy classifies all major encoding families - basis, angle, dense-angle, amplitude, data re-uploading, and IQP - along independently measurable axes. Second, closed-form depth-fidelity bounds under nisq decoherence channels identify the critical gate-error rate p* ~ 10^-3 below which amplitude encoding is viable. Third, a unified treatment of Fourier expressivity, barren-plateau onset, and quantum kernel concentration as functions of the encoding circuit provides the first joint trainability analysis. Fourth, a five-regime decision framework maps (D, n, p, tau) - feature dimension, qubit budget, error rate, and task type - to a hardware-grounded encoding recommendation. The central finding is that for p >= 10^-3, shallow angle-based encodings consistently outperform amplitude encoding in practice, despite the latter's exponential qubit advantage.