Further Reading: Quantum Classifiers

Tagged Tier 1 (confident it exists and recommended) and Tier 2 (real and worth seeking, but verify the current version or URL).

Data re-uploading

Pérez-Salinas, Cervera-Lierta, Gil-Fuster, and Latorre, "Data re-uploading for a universal quantum classifier" (2020), Quantum 4, 226. The paper §33.2 implements. Read it for the universality proof and for the geometric picture of a single qubit's Bloch-sphere trajectory — it is unusually clear, and the construction is more interesting than the accuracy numbers. Tier 1.
Schuld, Sweke, and Meyer, "Effect of data encoding on the expressive power of variational quantum machine learning models" (2021), Physical Review A 103, 032430. Shows that a re-uploading circuit computes a truncated Fourier series in the data, with the number of layers setting the number of accessible frequencies. This is the rigorous version of §33.2's "width is not what limits expressibility", and it explains the plateau Exercise 33.11 asks about. Tier 1.
Any treatment of universal approximation for neural networks (Cybenko, Hornik). The classical analogue, and the same caution applies: a universality theorem is about representability, not about what training finds. Tier 1.

Variational classifiers

Havlíček et al., "Supervised learning with quantum-enhanced feature spaces" (2019), Nature 567, 209. The paper that introduced both the variational classifier and the quantum kernel method Chapter 34 covers. Read it for the framing of the two approaches as alternatives. Tier 1.
Farhi and Neven, "Classification with quantum neural networks on near term processors" (2018), arXiv:1802.06002. An early and influential formulation. Worth reading against §33.4's results. Tier 1.
Chapter 16's and Chapter 32's barren-plateau reading. Trainability is the constraint that decides whether any of these architectures reach what they can represent. Tier 1.

On evaluating claims — the most important section here

Anything on the replication crisis and small-sample inference. §33.3's finding — a 0.13 gap becoming $+0.0202 \pm 0.0170$ — is a textbook small-sample effect, and the classical literature on it is enormous and directly applicable. Tier 1.
scikit-learn's documentation on cross-validation and cross_val_score. The standard protocol for exactly this problem, and it is one function call. If you take one practical thing from this chapter, take the habit of never reporting a single split. Tier 1.
Literature on nested cross-validation and the dangers of tuning on the test set. Exercise 33.23's subject, and the next mistake after the one this chapter makes. Tier 1.
Bouthillier et al. on accounting for variance in machine learning benchmarks (2021). Quantifies how much of a reported improvement is typically split-to-split noise. Sobering, and it is about classical ML — the problem is not specific to quantum. Tier 2.

Benchmarking quantum models honestly

Bowles, Ahmed, and Schuld, "Better than classical? The subtle art of benchmarking quantum machine learning models" (2024). Systematically re-runs published QML benchmarks with tuned classical baselines. The single most useful paper for calibrating expectations about this chapter's subject, and it reaches conclusions very close to §33.4's. Tier 1 — check for the current version.
Chapter 32 §32.8's seven-question checklist, applied to anything you read. Exercise 33.35 turns it on this chapter.

On the costs

Chapter 24 §24.3's shot budget and Chapter 32 §32.4's training budget. The inference bill in §33.6 is the third member of that family, and the one with no published analysis to point at — which is itself the finding. Tier 1.
Any treatment of total cost of ownership for deployed ML systems. Classical MLOps literature distinguishes training from serving cost as a matter of course; the quantum literature has not yet adopted the distinction, and it matters more here. Tier 2.

Backward references

Chapter 32 — the input problem, the training budget, and the checklist this chapter is built against.
Chapter 27 — two error rates, and why a small sample cannot resolve a small rate.
Chapter 28 — the other place in this book where two samples produced a conclusion that did not replicate.

Forward references

Chapter 34 — the technique with the cleanest mathematical story in Part VI, and a different argument.
Chapter 35 — where quantum data changes the calculation.

Where to go next. If one thing: Pérez-Salinas et al. on data re-uploading. It is short, the construction is genuinely surprising, and the Bloch-sphere picture makes it obvious why re-injecting the data buys expressibility that width does not.

If two: add Bowles, Ahmed, and Schuld on benchmarking QML models. It does at scale what §33.3 and §33.4 do on one problem — re-run published comparisons with tuned classical baselines — and the agreement between their conclusions and this chapter's is worth seeing for yourself.

Then Chapter 34, where the quantum feature map is used differently, and the mathematical case is stronger.