Entangling blocks in feature maps

Advanced Quantum Machine Learning

Created by Pavel · 17.03.2026 at 07:05 UTC

Product encodings keep qubits nearly independent; entangling layers mix them so similarity can depend on joint features—think classical lifts that add $x_1 x_2$. ZZ-style couplings are the circuit analogue.

Entanglement reshapes the hypothesis space; it does not, by itself, guarantee better test error.

University approvals: 0

Tasks

Question 1

What is the main purpose of adding an entangling block to a quantum feature map?

Hint

Focus on interactions between features.

To reduce all features to a single scalar

To introduce joint feature effects into the encoded geometry

To remove all phases from the circuit

To guarantee better accuracy on every dataset

Question 2

In a ZZ-style feature map, which two-qubit operator appears in the interaction block?

Hint

Use the Pauli observable mentioned in the lecture.

$X \otimes X$

$Y \otimes Y$

$Z \otimes Z$

$I \otimes I$

Question 3

What is the closest classical parallel to an entangling feature block that makes the kernel sensitive to joint feature effects?

Hint

Think of the nonlinear lift from the previous lecture.

Dropping all interaction terms

Adding a feature such as $x_1x_2$

Replacing inputs by labels

Increasing only the number of shots

Question 4

Which statement best contrasts product encoding with entangling encoding?

Hint

Compare what kinds of geometric dependence each construction can express.

Product encoding can encode amplitudes, but entangling encoding cannot

Product encoding often leads to strongly factorized similarity, while entangling encoding can make overlaps depend on feature interactions

Entangling encoding removes the need for state preparation

Product encoding always gives a better kernel on small datasets

Question 5

Implement classical_interaction_lift(x1: float, x2: float) -> float returning $x_1 \cdot x_2$. Raise TypeError if either arg is not int or float.

Hint

isinstance(x, (int, float))

def classical_interaction_lift(x1, x2):
    # TODO
    pass

Starter code is prefilled; replace TODO blocks with your solution.

Runtime output (stdout/stderr)

2 test cases will be used for grading

Run checks runtime behavior only. Final correctness is evaluated when you submit.

Card Info

Topic: Quantum Machine Learning
Difficulty: Advanced
Completed: 0 users

Creator

Pavel