Kernels, baselines, and re-uploading

Advanced Quantum Machine Learning

Created by Pavel · 17.03.2026 at 07:05 UTC

Kernel methods live on similarities, so honest evaluation compares quantum kernels to strong classical kernels on the same split. Re-uploading feeds data through the circuit more than once, enlarging the effective feature map—but expressivity still needs a useful inductive bias.

The failure mode is celebrating a flexible map that only memorises noise.

University approvals: 0

Tasks

Question 1

Which statement is correct?

Hint

A kernel is a similarity measure, not necessarily a distance.

Distance and kernel value are always the same number

A kernel can often be computed from an overlap without explicitly listing all lifted coordinates

Increasing distance always increases kernel value

A kernel matrix stores only diagonal entries

Question 2

Why can data re-uploading enrich a quantum model?

Hint

Think of the pattern: data, trainable transformation, data again.

It forces the Gram matrix to be diagonal

It guarantees quantum advantage

It creates a richer effective feature map than a single encoding pass

It removes the need for normalization in amplitude encoding

Question 3

According to the implementation workflow, what should be done after computing pairwise quantum similarities $K_{ij}$?

Hint

The comparison should be fair and use the same data split.

Assume the quantum model is automatically better

Compare against classical kernels under the same split

Discard all off-diagonal terms

Replace the labels by amplitudes

Question 4

Which statement about re-uploading is the most accurate?

Hint

More expressive does not mean automatically better.

It is useful only for basis encoding

It always lowers the cost of kernel estimation

It can increase expressivity, but a poor circuit design may still add little useful structure

It removes the role of trainable parameters

Question 5

Implement gram_upper_count(n: int) -> int returning the number of entries in the upper triangle of an $n\times n$ symmetric matrix including the diagonal ($i \le j$).

Hint

n*(n+1)//2

def gram_upper_count(n: int) -> int:
    # 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