Further Reading: Quantum Machine Learning Fundamentals

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

A caution specific to this chapter: QML has more published enthusiasm than published measurement. Read every result against §32.8's seven questions, and prefer sources that state their classical baseline.

The honest surveys

• Schuld and Petruccione, Machine Learning with Quantum Computers (2nd ed., 2021). The standard textbook, and unusually careful about what is and is not established. Its treatment of data encoding is the best available, and it takes the input problem seriously rather than waving at QRAM. Tier 1.
• Biamonte, Wittek, Pancotti, Rebentrost, Wiebe, and Lloyd, "Quantum machine learning" (2017), Nature 549, 195. The survey that defined the field's agenda. Read it, then read the dequantization literature below, because several of its headline speedups did not survive. Tier 1.
• Cerezo et al., "Variational Quantum Algorithms" (2021), Nature Reviews Physics 3, 625. Chapter 24's recommendation, equally relevant here — QML models are variational algorithms with a different cost function, and every obstacle transfers. Tier 1.
• Any recent critical review of QML's practical status. These exist, they are written by people inside the field, and they are more useful than the optimistic ones. Tier 2 — check dates.

On the input problem

The section that decides most of the argument.

• Aaronson, "Read the fine print" (2015), Nature Physics 11, 291. Two pages, and the single most important thing to read in this chapter's list. It lays out exactly the caveats §32.2 measures: input loading, output readout, and the conditions under which a quoted exponential speedup evaporates. Tier 1.
• Giovannetti, Lloyd, and Maccone on QRAM (2008). The architecture everything depends on. Read it alongside the analyses of what building one would actually cost. Tier 1.
• Any analysis of QRAM's error-correction requirements. The argument that a QRAM robust enough to be useful needs fault tolerance, at which point Chapter 25's overhead dominates. This is the strongest form of the objection. Tier 2.
• Chapter 15's resource estimator, applied to a QRAM-sized circuit. A concrete way to feel the cost. Tier 1.

Dequantization

The literature that most changed what QML claims.

• Tang, "A quantum-inspired classical algorithm for recommendation systems" (2019), STOC. The result that started it: a classical algorithm matching a celebrated quantum speedup, once the quantum algorithm's input assumptions were granted classically too. Read it for the method of argument — it is a lesson in what "speedup" means when the input model differs. Tier 1.
• The dequantization follow-ups — Chia, Gilyén, Li, Lin, Tang, Wang and others, extending the technique to principal component analysis, supervised clustering, and low-rank linear algebra generally. The common structure is worth extracting: low rank plus sampling access. Tier 1.
• Analyses of when dequantization does NOT apply. Equally important, and the boundary of the surviving quantum case. Tier 2.

On separations that survive

• Liu, Arunachalam, and Temme, "A rigorous and robust quantum speed-up in supervised machine learning" (2021), Nature Physics 17, 1013. A proven separation, on a constructed problem built on discrete-log structure. Read it for what a rigorous QML separation actually requires — and notice how specific the problem has to be. Tier 1.
• Huang et al. on the power of data in quantum machine learning (2021), Nature Communications. Argues that classical models given access to data can match quantum models on many tasks, and characterizes when they cannot. One of the most useful papers for calibrating expectations. Tier 1.
• Work on learning from quantum data — where the input is a physical state rather than a classical vector. The strongest surviving case, and Chapter 35's subject. Tier 2 — active.

Barren plateaus

• McClean, Boixo, Smelyanskiy, Babbush, and Neven, "Barren plateaus in quantum neural network training landscapes" (2018), Nature Communications 9, 4812. Chapter 16's foundational reference, and the mechanism §32.5 measures. Tier 1.
• Cerezo et al. on cost-function-dependent barren plateaus (2021). Local versus global cost functions, and why the choice matters. Exercise 32.27's subject. Tier 1.
• Chapter 16's and Chapter 24's further reading, entire. The plateau literature is the same literature.

Tooling

• PennyLane's documentation and demos. The library this chapter's classifier uses, and the best QML tooling available. Its demos are honest about limitations more often than most sources. Tier 1.
• scikit-learn's documentation on model selection. If you are comparing against a classical baseline, tune it — an untuned baseline is not a baseline, and §32.8's first question is about exactly this. Tier 1.
• Qiskit Machine Learning, for the Qiskit-native equivalents. Tier 2 — check maintenance status.

Backward references

• Chapter 16 — barren plateaus, first measured, and the parameter-shift rule's $2n+1$.
• Chapter 24 — the shot budget this chapter multiplies by a dataset.
• Chapter 29 — circuit shape, which applies to ansatz choice here.

Forward references

• Chapter 33 — classifiers in depth.
• Chapter 34 — the technique with the cleanest mathematical story in Part VI.
• Chapter 35 — where the quantum-data case is taken seriously.

Where to go next. If one thing: Aaronson's "Read the fine print." Two pages, written in 2015, and it anticipates every measurement in §32.2. It is the most efficient calibration available for reading QML claims.

If two: add Tang's dequantization paper, not for the algorithm but for the argument. It shows what happens when you grant a classical algorithm the same input access a quantum algorithm assumes — and that move is the one §32.2's input problem keeps forcing.

Then Chapter 33, which builds classifiers properly, with this chapter's checklist attached.