Self-Assessment Quiz: Quantum Machine Learning

Twenty questions on variational circuits, quantum kernels, data loading, barren plateaus, and the evidence base for QML. Aim for 16+.

Question 1

A parameterized quantum circuit used as a model is often called:

A) A quantum neural network or variational circuit B) An oracle C) A stabilizer D) A Trotter step

Question 2

The single largest obstacle to QML on classical data is:

A) Circuit depth B) Loading $N$ classical data points into quantum states C) Qubit count D) Measurement basis choice

Question 3

Amplitude encoding stores $2^n$ values in $n$ qubits, but:

A) Preparing the state generally costs $O(2^n)$ gates B) It is free C) It requires no qubits D) It is exact and cheap

Question 4

Angle encoding uses one rotation per feature, costing:

A) $O(2^n)$ B) $O(n)$ gates for $n$ features C) Nothing D) $O(n^2)$

Question 5

A quantum kernel method computes:

A) $|\langle\phi(x)|\phi(x')\rangle|^2$ between encoded data points B) A classical dot product only C) The Hamiltonian D) A gradient

Question 6

The kernel matrix for $M$ training points requires:

A) $O(M)$ circuit evaluations B) $O(M^2)$ C) $O(1)$ D) $O(\log M)$

Question 7

Barren plateaus in QML mean:

A) Gradients vanish exponentially with qubit count, preventing training B) Data is flat C) The model overfits D) Accuracy saturates

Question 8

Exponential concentration of quantum kernels means:

A) Off-diagonal kernel entries approach zero, making the kernel matrix near-identity B) Kernels become classical C) Training accelerates D) Data concentrates

Question 9

A near-identity kernel matrix causes:

A) Perfect generalization B) Memorization of training data with no generalization C) Faster training D) Lower variance

Question 10

"Dequantization" results by Tang and others showed:

A) Several claimed QML speedups have classical algorithms with comparable scaling B) QML is impossible C) Quantum computers are slower D) Kernels do not work

Question 11

Those results apply when:

A) The quantum algorithm assumes strong classical data-access structures (e.g. QRAM-like sampling) B) Never C) Only for images D) Only for small data

Question 12

The most defensible QML application area is:

A) Classifying classical images B) Learning on quantum data — states from experiments or simulations C) Large language models D) Recommendation systems

Question 13

Training a variational classifier requires gradients, typically obtained by:

A) The parameter-shift rule or finite differences B) Backpropagation through the quantum device C) Exact differentiation D) No gradients

Question 14

The parameter-shift rule costs:

A) Two circuit evaluations per parameter B) One evaluation total C) $2^n$ evaluations D) Zero

Question 15

Compared with classical deep learning, current QML models are:

A) Far smaller, with no demonstrated accuracy advantage on classical benchmarks B) Larger and more accurate C) Equivalent D) Faster to train

Question 16

True or false: QML has demonstrated advantage over classical ML on standard benchmarks.

Question 17

True or false: Backpropagation works on a quantum device the way it does on a GPU.

Question 18

True or false: Quantum kernels can express feature maps that are classically hard to compute.

Question 19

Short answer. Explain why data loading undermines most QML speedup claims on classical data.

Question 20

Short answer. Why is learning on quantum data a stronger proposition than learning on classical data?

Answer Key

Q Ans Note
1 A Both names are used; "quantum neural network" invites misleading analogies to classical networks.
2 B The input problem, not the processing, is the bottleneck.
3 A Exponentially compact storage, exponentially expensive preparation — the trade that defeats naive proposals.
4 B Cheap, which is why it dominates in practice, at the cost of using only $n$ features for $n$ qubits.
5 A The squared overlap of encoded states is a valid kernel.
6 B Quadratic in dataset size, each entry a circuit evaluation with shot noise — expensive for realistic $M$.
7 A The same phenomenon as in VQE, and arguably more damaging since QML models need many parameters.
8 A For expressive encodings, overlaps between distinct data points concentrate near zero exponentially in $n$.
9 B A near-identity kernel says every point is similar only to itself — the model memorizes and cannot generalize.
10 A Tang's recommendation-systems result and its successors.
11 A The dequantized classical algorithms assume analogous sampling access, so the comparison is apples to apples — and the quantum advantage largely disappears.
12 B Quantum data avoids the loading bottleneck entirely; this is the area with a defensible argument.
13 A Parameter-shift gives exact gradients using the same circuit at shifted parameters.
14 A Two evaluations per parameter per step — so gradient cost is linear in parameter count, versus effectively constant for classical backprop.
15 A Current QML models have dozens of parameters against billions classically, with no benchmark advantage.
16 False No standard-benchmark advantage exists. Reported wins are typically on tiny datasets, contrived tasks, or against weak classical baselines.
17 False Backprop requires storing intermediate activations; measurement destroys quantum states, and no-cloning forbids copying them. Parameter-shift is the substitute and is far more expensive — a structural, not engineering, difference.
18 True This is the genuine theoretical appeal: some quantum feature maps are classically hard to evaluate. Whether such maps are useful for real learning tasks is the open question.
19 — A quantum speedup must be measured end to end. Amplitude encoding of $N$ features costs $O(N)$ gates, which already matches or exceeds the classical algorithm's cost for many tasks. QRAM proposals move that cost into hardware requiring $O(N)$ components. And for classical data the classical algorithm can simply read the data directly. Any claim of exponential QML speedup on classical data must specify how the data enters the quantum computer, and that step usually consumes the advantage.
20 — Quantum data — states produced by an experiment, a sensor, or a simulation — is already in quantum form, so there is no loading cost and no classical description to compare against. Tasks such as learning properties of an unknown state, classifying phases of matter from prepared states, or learning a physical process from its action on probe states have no efficient classical analogue because the classical description of the input is itself exponentially large. This is where QML's theoretical arguments are strongest and where early advantage, if any, is most likely.