Further Reading: Transpilation

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

Quantum compilation is one of the healthiest research areas in the field — the problems are well-posed, progress is measurable, and improvements transfer immediately to every user. It is also a good area for a classically-trained software engineer to contribute to, which Chapter 40 argues at length.

The primary sources

• The Qiskit transpiler documentation. Pass managers, the six stages, every built-in pass, and the preset configurations. The generate_preset_pass_manager page in particular documents exactly what each optimization level does — worth reading once so that "level 3" stops being a magic number. Tier 1.
• The Qiskit documentation on writing a custom pass. TransformationPass, AnalysisPass, property_set, and the DAG API. Short, and §10.8's examples come from it. Tier 1.
• The qiskit.dagcircuit API reference. op_nodes, layers, collect_runs, substitute_node_with_dag, remove_op_node. This is the vocabulary of every pass you will write. Tier 1.

On routing and layout

The algorithms behind §10.6, and the reason the method choice matters.

• Li, Ding, and Xie, "Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices" (2019), ASPLOS. The SABRE paper — the algorithm that wins in §10.6's comparison. Its key idea is to run routing forward and backward to refine the initial layout, rather than choosing a layout and then routing into it. Readable, and it explains why SABRE beats dense by co-designing the two decisions. Tier 1.
• Cowtan et al., "On the Qubit Routing Problem" (2019), TQC. A careful treatment of routing as an optimization problem, with complexity results and a comparison of approaches. The reference for §10.6's claim that routing is NP-hard. Tier 1.
• Any recent survey of qubit mapping and routing. This is an active area with a steady stream of new heuristics; searching "qubit mapping problem survey" finds the current state. If your circuits are routing-limited — measurable in one line with routing_overhead from Case Study 1 — it is worth reading recent work rather than accepting defaults. Tier 2.
• The VF2 subgraph isomorphism algorithm, and Qiskit's VF2Layout / VF2PostLayout passes. When a perfect layout exists (no routing needed), VF2 finds it and scores candidates by error rate. This is what saved the $n=7$ GHZ state in Chapter 4's Case Study 1. Tier 2 — pass names have moved across releases.

On gate synthesis and basis translation

The §10.2 material, treated properly.

• Barenco et al., "Elementary Gates for Quantum Computation" (1995), Physical Review A 52, 3457. Already recommended in Chapter 3; it is the foundation of basis translation, multi-controlled gate decomposition, and the two-qubit constructions Chapter 28 optimizes. Tier 1.
• The Solovay–Kitaev theorem, for approximating arbitrary gates from a discrete set. Relevant when the target basis is discrete (fault-tolerant Clifford+T) rather than continuous, which is the regime Chapter 23's resource estimates live in. Nielsen and Chuang §4.5.3. Tier 1.

On the heavy-hex topology

§10.1's claim that sparsity is deliberate.

• IBM's published rationale for the heavy-hexagonal lattice. The move from a denser square lattice was driven by frequency collisions and crosstalk — the sparser layout has worse connectivity and better gate fidelity, which is exactly the trade §10.1 describes. Search IBM Research's blog and papers on heavy-hex code and lattice design. Tier 2.
• Chamberland et al., "Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits" (2020), Physical Review X 10, 011022. The error-correction argument for heavy-hex: low-degree connectivity is not merely tolerable but advantageous for certain codes. The deeper reason the topology looks the way it does. Tier 1.

On reproducibility (Case Study 2)

• Any of the ongoing discussions of reproducibility in computational science. The quantum-specific list — versions, seeds, layouts, calibration windows, shots, mitigation settings — is longer than most fields' but the principles are standard. Tier 2.
• Your target journal's reproducibility guidance for quantum submissions. Increasingly explicit about exactly the provenance fields §10.9 lists. Read it before writing up, not after. Tier 2.
• Chapter 30 §30.8 formalizes the fair-comparison protocol that Case Study 2's hardest question asks you to design. Tier 1.

Forward references

• Chapter 28 goes deeper on the optimization stage: cancellation, commutation, template matching, and unitary synthesis, with custom passes built on §10.8's foundation.
• Chapter 29 covers noise-aware layout selection properly, plus the scheduling stage this chapter only names.
• Appendix G collects the topology and calibration reference material: how to read a coupling map, what the error fields mean, and the basis gate sets of the major device families.

Where to go next. If one thing: the SABRE paper. It is the algorithm doing the work in every transpilation you run, and understanding why it co-designs layout with routing is the single insight that makes the rest of this chapter's measurements predictable rather than surprising.

Then Chapter 11 — simulators and noise models.