Further Reading: Hybrid Architectures

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

Part VI's last reading list, and the one with the most live research in it — because the quantum-data case is the part of QML that has not been closed off.

Classical shadows

• Huang, Kueng, and Preskill, "Predicting many properties of a quantum system from very few measurements" (2020), Nature Physics 16, 1050. The paper §35.5 implements. Read it for the sample-complexity bound and its dependence on observable locality — that dependence is the whole reason the technique works, and it is also its limit. Tier 1.
• Follow-up work on derandomized and locally-biased shadows. Improvements when you know in advance which observables you want, which is the common case in chemistry. Tier 2 — active.
• Chapter 24 §24.3's shot budget. Shadows are the only technique in this book that attacks it from the estimates-per-shot side; everything else fought $1/\epsilon^2$ directly and lost. Tier 1.

Learning from quantum data

The strongest surviving case, and where the interesting results are.

• Huang, Broughton, Cotler, Chen, Li, Mohseni, Neven, Babbush, Kueng, Preskill, and McClean, "Quantum advantage in learning from experiments" (2022), Science 376, 1182. An exponential separation for learning tasks where the learner can process quantum data coherently, with hardware demonstrations. The most important paper in this chapter's list, and Exercise 35.27's subject — read it asking exactly what is being compared and whether the input problem applies. Tier 1.
• Cotler, Huang, and McClean on revisiting dequantization and quantum advantage in learning. The careful boundary between tasks that dequantize and tasks that do not. Tier 2.
• Literature on classifying phases of matter with machine learning, classical and quantum. §35.2's task is a standard benchmark in this area, and the classical results are strong — which is the context §35.4's baseline sits in. Tier 2.
• Work on quantum sensing and metrology as a learning problem. Where the input is unavoidably quantum and there is no classical alternative at all. Tier 2 — a different framing of the same advantage.

Hybrid runtimes and the practical loop

• Qiskit Runtime's documentation, and the equivalent primitives from other vendors. The architectural fix to §35.6's latency problem — the classical update runs next to the device so the loop closes without a round trip. Tier 1.
• Chapter 31's coherence budget and Chapter 33's inference bill. Together they are the production cost model: circuit time is microseconds, queue latency is seconds, and shots are forever. Tier 1.
• Literature on circuit knitting and distributed quantum computing. Cutting a large circuit into device-sized pieces with classical post-processing — a different placement of the same boundary this chapter is about. Tier 2 — active, and the reconstruction cost grows exponentially in the number of cuts.

The honest overviews of QML

Worth reading now that Part VI is complete, because they land differently.

• Schuld and Killoran, "Is quantum advantage the right goal for quantum machine learning?" (2022), PRX Quantum 3, 030101. Argues the field should stop chasing speedup comparisons and study what quantum models are. Read it against Part VI's scorecard — it is the most thoughtful response to exactly the results these four chapters measured. Tier 1.
• Aaronson, "Read the fine print" (2015). Chapter 32's recommendation, and it holds up completely. Tier 1.
• Bowles, Ahmed, and Schuld on benchmarking QML models (2024). The systematic version of Part VI's comparisons. Tier 1.

Backward references

• Chapter 32 — the input problem this chapter's data avoids, and the $N-\log_2 N-1$ encoding cost.
• Chapter 33 — the replication protocol and the inference bill, both of which still apply.
• Chapter 34 — convex training, and the $n^2$ that replaced it.
• Chapter 26 — the 30–35 qubit simulation boundary that decides §35.4.

Forward references

• Chapter 36 — Part VII opens on chemistry, where the data is quantum by nature and Chapter 24's VQE produces exactly the states this chapter classified.

Where to go next. If one thing: Huang et al., "Quantum advantage in learning from experiments." It is the strongest result in the direction this chapter identifies as the surviving one, it includes hardware demonstrations, and it is specific about what is being compared — which after Part VI you are well equipped to check.

If two: add Schuld and Killoran on whether advantage is the right goal. Part VI has spent four chapters measuring quantum models against classical baselines and finding them behind; that paper argues the exercise is the wrong one, and it is worth taking seriously by someone who has just done the exercise.

Then Chapter 36, where Part VII begins — and where quantum data stops being a special case and becomes the whole subject.