Further Reading: Pulse-Level Programming, and What Replaced It

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: more of this reading list is stale than in any other chapter of this book, and that is the chapter's subject. Anything describing qiskit.pulse is describing a removed API. Read it for the physics, not for the code.

What replaced the pulse API

• The Target API documentation — target.dt, target[gate][qubits].duration, and qubit_properties[q].t1/.t2. This is where every number in §31.1 and §31.2 comes from, and it is the supported replacement for what backend.defaults() used to provide. Tier 1.
• Qiskit's scheduling documentation — ASAPScheduleAnalysis, ALAPScheduleAnalysis, PadDelay, PadDynamicalDecoupling. The surviving control surface. Tier 1.
• The Qiskit 1.x deprecation notices and the 2.0 migration guide. Worth reading once as an artifact: a careful, well-signposted removal of a major subsystem, and a model for how to do it. Tier 1.
• Qiskit Dynamics. Simulates the underlying Hamiltonian rather than a gate-level noise channel — which is the tool that could actually answer §31.4's question, and Exercise 31.32's subject. Tier 1.

The physics the removed API exposed

Still true, still worth knowing, and now read rather than programmed.

• Krantz, Kjaergaard, Yan, Orlando, Gustavsson, and Oliver, "A Quantum Engineer's Guide to Superconducting Qubits" (2019), Applied Physics Reviews 6, 021318. The single best reference for this chapter's physics — transmons, drive Hamiltonians, why gates are shaped pulses, and where $T_1$ and $T_2$ come from. Long, and worth it. Tier 1.
• Motzoi, Gambetta, Rebentrost, and Wilhelm on DRAG pulses (2009), Physical Review Letters 103, 110501. Why a square envelope leaks population into $|2\rangle$ and how a derivative correction fixes it. Exercise 31.31's subject. Tier 1.
• McKay, Wood, Sheldon, Chow, and Gambetta, "Efficient Z gates for quantum computing" (2017), Physical Review A 96, 022330. The virtual Z gate — why rz takes zero time and is exactly error-free, and why the $\{$rz, sx, x$\}$ basis looks the way it does. Short, and it explains the most surprising number in the chapter. Tier 1.
• Any treatment of the cross-resonance interaction, which is what ecr implements and why two-qubit gate durations vary from 341 to 882 ns across a chip while single-qubit gates are uniform. Tier 2.

Dynamical decoupling

The section where the reading matters most, because the simulation cannot substitute for it.

• Viola, Knill, and Lloyd, "Dynamical decoupling of open quantum systems" (1999), Physical Review Letters 82, 2417. The foundational result. Read the assumption about the noise spectrum — it is exactly what §31.5 found missing from a Markovian model, stated by the original authors. Tier 1.
• Literature on the filter-function formalism for decoupling sequences. Makes the point quantitatively: a DD sequence is a high-pass filter on the noise spectrum, so its benefit depends entirely on how much noise power sits at low frequency. A white (Markovian) spectrum has nothing to filter. This is the rigorous version of §31.5. Tier 1.
• Any experimental paper measuring DD on superconducting hardware, especially ones reporting the improvement as a function of idle duration. These are the measurements §31.4 could not make, and reading one alongside this chapter's negative result is the most instructive pairing available. Tier 1.
• Work on $1/f$ flux noise in superconducting qubits. The specific noise DD is fighting, and why it is correlated over microseconds. Tier 2.

On depending on things that disappear

• Hyrum's Law, and the broader literature on API stability and deprecation policy. Case Study 1 in general form. Tier 1.
• Chapter 27's further reading on property-based and regression testing. The defence against API removal is a test that imports what you depend on, and it costs nothing. Tier 1.
• Any discussion of reproducibility in computational research. Research code pinned below Qiskit 2.0 still runs and gets harder to build on every year — a decay clock, not a solution. Tier 2.

Backward references

• Chapter 12 — the measured gate error that makes this device gate-error-limited rather than decoherence-limited.
• Chapter 25 — the syndrome cycle whose cost is measurement-bound, at 1,216 ns per readout.
• Chapter 26 — "debug on a simulator, validate on hardware," to which this chapter adds the corollary.
• Chapter 30 — where $T_1$, $T_2$ and the gate durations come from, and how much they move.

Forward references

• Chapter 32 — Part VI opens, and every constraint from Part V applies at once.

Where to go next. If one thing: McKay et al. on virtual Z gates. It is short, it explains why rz costs zero time and zero error, and once you have read it the structure of every transpiled circuit in this book makes sense.

If two: add Viola, Knill, and Lloyd on dynamical decoupling, read specifically for its assumptions about the noise spectrum. §31.5's conclusion — that DD cannot help against memoryless noise — is not a discovery of this chapter; it is a condition the original paper states, and which a Markovian simulator silently violates.

Then Chapter 32, where Part VI begins and Chapter 24's shot budget, Chapter 16's barren plateaus, and this chapter's coherence budget all arrive together.