Project 11: Quantum Machine Learning (QML) - Kernel Methods

Build a quantum kernel demo and compare it to a classical kernel.

Project Overview

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 1-2 weeks
Main Language Python
Alternative Languages Julia, R
Knowledge Area Quantum machine learning
Tools Qiskit or Cirq
Main Book “Quantum Machine Learning” by Maria Schuld and Francesco Petruccione

What you’ll build: A small dataset classification demo using a quantum kernel and a classical SVM.

Why it teaches quantum: QML is mostly about feature maps and kernel evaluation via circuits.

Core challenges you’ll face:

  • Building a feature map circuit
  • Estimating kernel entries via circuit overlaps
  • Comparing to classical baselines

Real World Outcome

You will train a kernel classifier and report accuracy compared to a classical kernel.

Example Output:

$ python qml_kernel.py --dataset moons
Quantum kernel accuracy: 0.86
Classical RBF accuracy: 0.84

Verification steps:

  • Ensure kernel matrix is symmetric and positive semi-definite
  • Compare results over multiple runs

The Core Question You’re Answering

“How can a quantum circuit define a feature space for classification?”

This is the heart of quantum kernel methods.

Concepts You Must Understand First

Stop and research these before coding:

  1. Kernel methods
    • Why do kernels replace explicit feature maps?
    • Book Reference: “Quantum Machine Learning” by Schuld & Petruccione, Ch. 6
  2. Feature map circuits
    • How do you encode classical data into quantum states?
    • Book Reference: “Quantum Machine Learning” by Schuld & Petruccione, Ch. 4
  3. Kernel estimation
    • How do you estimate overlaps using circuits?
    • Book Reference: “Quantum Machine Learning” by Schuld & Petruccione, Ch. 6

Questions to Guide Your Design

  1. Dataset choice
    • Which small dataset will you use (moons, circles)?
    • How will you normalize features?
  2. Evaluation
    • How will you compare to classical kernels fairly?
    • Will you report accuracy or F1?

Thinking Exercise

Kernel Symmetry

Why must the kernel matrix be symmetric? What would it mean if it isn’t?

Questions while working:

  • How does symmetry relate to inner products?
  • What does positive semi-definite imply?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is a kernel method?”
  2. “How do quantum kernels work?”
  3. “What is a feature map in QML?”
  4. “How do you estimate kernel entries?”
  5. “What are the limitations of QML today?”

Hints in Layers

Hint 1: Starting Point Start with a tiny dataset and 2 qubits.

Hint 2: Next Level Compute the kernel matrix on a simulator.

Hint 3: Technical Details Use the kernel matrix as input to a classical SVM.

Hint 4: Tools/Debugging Check kernel symmetry and eigenvalues.

Books That Will Help

Topic Book Chapter
Kernel methods Schuld & Petruccione Ch. 6
Feature maps Schuld & Petruccione Ch. 4
Kernel estimation Schuld & Petruccione Ch. 6

Implementation Hints

  • Keep datasets small to reduce kernel computation time.
  • Use a classical SVM as baseline.
  • Repeat runs to account for sampling noise.

Learning Milestones

  1. First milestone: You can build a feature map circuit.
  2. Second milestone: You can compute a quantum kernel matrix.
  3. Final milestone: You can compare quantum vs classical performance.