Quantum Machine Learning

The core loop of near-term QML: encode data into a circuit, apply parameterized gates, measure an expectation value, compute a loss, update parameters - gradient descent on gate angles.

Study

• PennyLane QML demos: start with the qubit rotation tutorial, then variational classifier.
• Schuld & Petruccione, Machine Learning with Quantum Computers: chapters on information encoding - angle encoding vs amplitude encoding vs basis encoding. This choice will dominate Capstone B.
• Paper: Schuld et al. - Circuit-centric quantum classifiers (from your list).

Exercises

• Build a variational classifier in PennyLane for a 2D toy dataset (moons); plot its decision boundary next to your Week 3 k-NN.
• Encode a 4-dimensional feature vector by angle encoding on 4 qubits, and by amplitude encoding on 2 qubits; verify both states in the simulator.
• Compute a gradient with the parameter-shift rule by hand for one gate; verify against PennyLane's autograd.

Checkpoint

You can state the cost, in qubits and circuit depth, of amplitude-encoding a 128-sample I/Q frame - and why that cost is the central obstacle for quantum radio ML.

The other pillar of QML: treat the quantum state as a feature map and compute kernels classically-inaccessibly. Two of your listed papers are this week's reading.

Study

• Papers: Schuld & Killoran - Quantum machine learning in feature Hilbert spaces and Havlicek et al. - Supervised learning with quantum-enhanced feature spaces (the Nature paper from your list).
• Qiskit Machine Learning tutorials: quantum kernels and QSVC.

Exercises

• Train a QSVC with a quantum kernel on a small dataset; compare against a classical RBF-kernel SVM on the same data. Report both numbers honestly.
• Compute a 2x2 quantum kernel matrix by hand (two data points, angle encoding, inner product of states); verify in code.

Checkpoint

You can explain in one paragraph what would need to be true of a dataset for a quantum kernel to beat all classical kernels - and why nobody has convincingly shown it on natural data yet.

The week that separates people who can read QML headlines from people who can evaluate them. Three papers, all from your list, in the right order.

Study

• McClean et al. - Barren plateaus in quantum neural network training landscapes: why random deep circuits have exponentially vanishing gradients.
• Cong, Choi, Lukin - Quantum Convolutional Neural Networks: THE QCNN paper. Hierarchical structure, logarithmic depth, pooling by measurement.
• Pesah et al. - Absence of barren plateaus in QCNNs: the reason the architecture you came here for is considered trainable.

Exercises

• Reproduce a mini barren-plateau experiment: for random circuits of 2, 4, 6, 8 qubits, sample the variance of a gradient component; plot variance vs qubit count on a log scale and watch it die.
• Diagram the Cong QCNN on paper: convolution layers as brickwork two-qubit unitaries, pooling as measure-and-condition. Annotate qubit counts layer by layer for an 8-qubit input.

Checkpoint

You can explain to a classical-ML friend what a barren plateau is, and the structural property of QCNNs that avoids it.

Study

• PennyLane: Generalization in QML from few training data - implements the Cong-style QCNN end to end; this is your reference implementation.
• PennyLane: Quanvolutional neural networks - the other "quantum CNN": a quantum layer inside a classical CNN. Know the difference; people conflate them constantly.

Exercises

• Implement an 8-qubit QCNN in PennyLane and train it on a simple task (downscaled digits or your toy signal features). Get the training curve to actually descend.
• Swap the QCNN ansatz for a random deep ansatz of equal parameter count; compare trainability. You should see Week 24's theory in your own loss curves.

Checkpoint

Your QCNN trains, and you can name every design decision in it (encoding, ansatz, measurement, loss) with a reason.