A variational quantum model is a small parameterized circuit inside an ordinary training loop. Classical code prepares features, updates parameters, and scores a loss. The quantum step only turns a state into samples or expectation values.
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Lesson close · Quantum Machine Learning
Consolidate QML Map & Hybrid Pipelines
Use this checkpoint to recall the lesson before marking it complete. The concepts below come from this lesson's authored sections.
Key concepts covered
01Development
02Worked examples
03Where this is used
04Pitfalls
What you should know now
□Explain QML Map & Hybrid Pipelines in your own words and state the assumptions.
□Reproduce the main argument, derivation, or implementation without copying the lesson.
□Check one example against units, boundary conditions, or edge cases.
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Progress
Name one modeling or implementation limitation and when it matters.
Sequence
Continue to Data Encoding & Re-uploading, the next prerequisite step in this course.
a measurement of an observable O, producing y^(x,θ)=⟨ψ∣O∣ψ⟩ with ∣ψ⟩=V(θ)U(ϕ(x))∣0⟩;
a classical loss L(θ) on those numbers and labels, and a classical update of θ.
Hypotheses. The device (or simulator) returns estimates of y^ from finitely many shots, not the vector ∣ψ⟩. θ is stored and updated classically. A holdout split is applied to classical pairs (x,y) before any claim about generalization.
Development
The loop is the same shape as a neural net with a peculiar layer. Features ϕ(x) are computed on a CPU. Encoding writes them into gate angles or into amplitudes. The ansatz is a product of gates whose angles are θ. Measuring O — often a Pauli Z on one qubit — yields a number in [−1,1] if O is that Pauli. A batch loss might be
L(θ)=∣B∣1i∈B∑(yi−y^(xi,θ))2.
The optimizer proposes θt+1 from L and from estimates of ∇θL. Those estimates are classical post-processing of shot averages (parameter shifts or finite differences).
Why the optimizer stays classical: the device returns shot estimates of y^, not a stored gradient you can iterate, and the data set does not fit in the register. Two evaluations at the same θ differ by shot noise. Different shot budgets are not the same experiment.
Worked examples
Where this is used
A research check “does this feature set beat logistic regression on a later month?” is this pipeline with a time-ordered holdout. The quantum piece is only U and V. The comparison is classical, on the same metric and the same dates.
Pitfalls
Loading the full data matrix into one quantum state and then talking about i.i.d. rows.
Tuning θ on every row you will quote as a test score.
Comparing a 200-shot run with an 8000-shot run as if both estimates of ⟨O⟩ had the same noise.
Interactive · classical↔quantum split
quantum=0.50 · classical=0.50
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