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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 35Day 967

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Year 2·Month 35·Week 3

Day 967: Quantum Feature Maps & Embeddings

Day 967 of 2,016~16 min read

Learning Objectives

  • •**Define quantum feature maps** and their role in quantum machine learning
  • •**Construct embedding circuits** that encode classical data into quantum states
  • •**Analyze the expressivity** of different feature map designs
  • •**Calculate inner products** between quantum-embedded data points
  • •**Implement basic feature maps** in PennyLane with proper parameterization
  • •**Compare quantum and classical** feature space representations

Today's Schedule (7 hours)

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Year 2 Semester 2B Fault Tolerance HardwareMonth 35 Advanced Algorithms - Week 139 QML FoundationsSchedule OverviewLearning ObjectivesMorning Session Theory 3 hours1 Introduction to Quantum Feature MapsThe Classical Machine Learning PerspectiveThe Quantum Generalization2 Mathematical FrameworkThe Feature Hilbert SpaceDensity Matrix Representation3 Common Feature Map Architectures31 Angle Encoding Basis Rotation32 Amplitude Encoding33 Product Feature Map Tensor Product34 ZZ Feature Map Entangling35 IQP Instantaneous Quantum Polynomial Encoding4 Designing Feature Maps Key Considerations41 Expressivity42 Injectivity43 Periodic Structure5 Connection to Classical Machine LearningThe Kernel CorrespondenceWhen Quantum HelpsAfternoon Session Problem Solving 2 hoursWorked Example 1 Single-Qubit Feature Map AnalysisWorked Example 2 Two-Qubit Product Feature MapWorked Example 3 Effect of EntanglementPractice ProblemsProblem 1 Basic Feature Map Direct ApplicationProblem 2 Data Scaling IntermediateProblem 3 Expressivity Analysis ChallengingEvening Session Computational Lab 2 hoursLab Implementing Quantum Feature Maps in PennyLaneExpected OutputSummaryKey FormulasKey TakeawaysConnection to Classical MLDaily ChecklistPreview Day 968
Day 966Day 967 of 2,016Day 968