Encoding classical data into quantum states

Intermediate Quantum Machine Learning

Created by Pavel · 17.03.2026 at 07:05 UTC

Classical vectors become quantum states through deliberate encoding choices: basis labels for discrete data, amplitudes subject to normalisation, or rotation angles on the Bloch sphere. Each choice trades interpretability against preparation cost.

Angle encoding that only applies $R_z$ without creating superposition leaves Z-measurement statistics unchanged—a common student trap when checking whether data actually entered the model.

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Tasks

Question 1

Which encoding maps a binary string directly to a computational-basis state such as $01 \mapsto |01\rangle$?

Hint

Choose the most literal encoding of a bitstring.

Basis encoding

Amplitude encoding

Angle encoding

Data re-uploading

Question 2

Which statement best describes the main attraction of amplitude encoding?

Hint

Think about compact storage versus preparation cost.

It works only for binary features, but it is noise-free

It can represent $2^n$ amplitudes with $n$ qubits, but general state preparation may be expensive

It always produces a separable state with no preprocessing

It avoids the need to normalize input data

Question 3

What condition must a classical vector satisfy before it can be used directly as amplitudes of a quantum state?

Hint

A quantum state must have total probability 1.

All entries must be integers

The entries must sum to zero

The vector must be normalized to unit norm

The vector must contain only positive values

Question 4

In angle encoding, where do classical features usually appear?

Hint

Look at one-qubit rotation gates.

As labels assigned to qubits

As parameters of gates such as $R_y(x_i)$ or $R_z(x_i)$

As measurement outcomes sampled at the end

As ancilla qubits appended after the circuit

Question 5

Implement amplitude_squared_norm(values: list[float]) -> float returning $\sum_i x_i^2$ (used to check whether a real vector can be turned into amplitudes before normalisation).

Hint

Sum squares in a loop or with comprehension.

def amplitude_squared_norm(values: list[float]) -> float:
    # 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: Intermediate
Completed: 0 users

Creator

Pavel