🎯 Quantum Kernel Methods
Exponential feature spaces for machine learning
Your Progress
0 / 5 completed🚀 The Kernel Trick, Quantumly
The kernel trick enables classification in high-dimensional spaces without explicit computation—evaluating inner products K(x,y) = ⟨φ(x), φ(y)⟩ in exponential dimensions. Quantum kernel methods use quantum computers to access feature maps φ that are impossible to compute classically, providing exponential advantage for pattern recognition.
💡 Why Quantum Kernels?
Classical kernels (RBF, polynomial) map to fixed dimensions. Quantum feature maps embed data into 2^n dimensional Hilbert space using n qubits—exponentially large without explicit computation. A 10-qubit quantum kernel accesses 1024-dimensional space; 20 qubits = 1 million dimensions.
🎯 What You'll Learn
📊 Kernel Methods Overview
Choose kernel k(x,y) (RBF, polynomial) → compute Gram matrix K → train SVM or classifier
Design quantum feature map U(x) → compute K(x,y) = |⟨0|U†(x)U(y)|0⟩|² on quantum device → train classically
Access feature spaces provably hard to compute classically—exponential separation for certain problems
🔬 Key Insight: Separation
Quantum kernels separate classes better when data has quantum structure (molecular properties, quantum sensor data) or high-dimensional correlations classical kernels miss. The advantage isn't universal—it's problem-dependent, with proven separations for specific tasks.