qml-feature-encoding

# QML Feature Encoding ## Description Quantum Machine Learning feature encoding methodology based on systematic review of 66 primary works (2017-2026). Provides a three-axis taxonomy (cost-expressivity-robustness), closed-form depth-fidelity bounds under NISQ decoherence channels, unified trainability analysis linking Fourier expressivity/barren-plateau/kernel concentration, and a five-regime decision framework mapping (feature dimension, qubit budget, error rate, task type) to hardware-grounded encoding recommendations. ## Activation Keywords - quantum feature encoding - qml data encoding - quantum data loading - amplitude encoding - angle encoding - quantum machine learning encoding - 量子特征编码 - 量子数据编码 - qml encoding strategy - NISQ encoding ## Tools Used - terminal: Run quantum circuit simulations - web_search: Find encoding literature - browser: Access quantum computing platforms ## Usage Patterns ### Pattern 1: Encoding Selection on NISQ Hardware Given device parameters (D=feature dimension, n=qubits, p=error rate, τ=task type): 1. Check if p >= 10^-3 → use shallow angle-based encoding 2. If p < 10^-3 and n >= log2(D) → amplitude encoding viable 3. For classification tasks → IQP encoding 4. For regression → data re-uploading ### Pattern 2: Trainability Analysis For a given encoding circuit: 1. Compute Fourier expressivity as function of encoding depth 2. Estimate barren-plateau onset via gradient variance scaling 3. Check quantum kernel concentration via spectral norm 4. If all three pass → encoding is trainable ### Pattern 3: Depth-Fidelity Bound Given gate error rate p and circuit depth d: - Critical threshold: p* ~ 10^-3 - If p >= p*: fidelity degrades exponentially with depth - Recommendation: keep depth < O(1/p) ## Instructions for Agents ### Step 1: Characterize the Problem Determine: - Feature dimension D - Available qubits n - Hardware error rate p (from calibration data) - Task type τ (classification, regression, clustering) ### Step 2: Apply Five-Regime Decision Framework | Regime | Conditions | Recommended Encoding | |--------|-----------|---------------------| | 1 | p >= 10^-3, D small | Shangle encoding | | 2 | p >= 10^-3, D large | Dense-angle encoding | | 3 | p < 10^-3, n >= log2(D) | Amplitude encoding | | 4 | p < 10^-3, n < log2(D) | Data re-uploading | | 5 | Any p, structured data | IQP encoding | ### Step 3: Verify Trainability Before committing to encoding: 1. Check Fourier spectrum coverage 2. Verify gradient doesn't vanish (barren plateau check) 3. Ensure kernel matrix isn't concentrated ### Step 4: Optimize Circuit Depth Minimize depth while maintaining expressivity: - Use basis encoding for binary features (depth=0) - Use angle encoding for continuous (depth=D) - Avoid deep amplitude encoding on NISQ ## Error Handling ### Amplitude Encoding on Noisy Hardware If p >= 10^-3 and amplitude encoding chosen: - Expect exponential fidelity decay - Fall back to angle encoding with depth O(D) - Trade qubit advantage for noise robustness ### Barren Plateau Detected If gradients vanish exponentially: - Reduce encoding depth - Try local cost functions - Use layerwise training ## Resources - arXiv: 2606.05387 — "Feature Encoding in Quantum Machine Learning: A Survey and Practical Guidelines" - PRISMA-adapted protocol for systematic QML encoding review