Further Reading: Qubit Manipulation in Code

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

This chapter's material is the most stable in the entire book — gate matrices have not changed since the 1990s and will not change. That makes older sources unusually safe here, which is not true anywhere else in this book.

The reference material you will actually use

Appendix B of this book. Every gate matrix, circuit symbol, Bloch rotation, and the identities worth memorizing ($HZH = X$, $HXH = Z$, $T^4 = Z$, $SS = Z$). Designed to be the page you keep open. Tier 1.
Appendix D. Complex numbers, vectors, matrices, inner products, and unitarity, covering exactly what this book uses. If §3.8 felt like hard work, read this before Chapter 4 — the tensor product section there is genuinely necessary. Tier 1.
The Qiskit circuit library API reference. The authoritative list of every gate Qiskit provides, with matrices. Faster to search than any book. Tier 1.

On the concepts

Nielsen and Chuang, Quantum Computation and Quantum Information, §1.3 and §4.2. The standard treatment of single-qubit gates, the Bloch sphere, and the rotation operators. §4.2's derivation of the $Z$–$Y$ decomposition is exactly Case Study 2's construction, done properly. Tier 1.
Nielsen and Chuang, §4.5. Universality, including the Solovay–Kitaev theorem referenced in Case Study 2's 🔬 Honest Assessment. Read it for the precise statement of what universality buys and what it does not. Tier 1.
John Watrous, lecture notes on quantum information (available free online). Unusually careful and precise about the things that trip people up — global versus relative phase, what "indistinguishable states" means operationally, and why the Bloch sphere is a two-to-one picture. If you like your foundations rigorous, start here. Tier 2 — hosted material moves.

On the Bloch sphere specifically

The Bloch sphere article on Wikipedia. Genuinely good, including the derivation of the Cartesian coordinates $(2\,\mathrm{Re}(\alpha^\beta),\ 2\,\mathrm{Im}(\alpha^\beta),\ |\alpha|^2-|\beta|^2)$ used in §3.4, and an honest treatment of the mixed-state interior. Tier 2.
Any interactive Bloch sphere visualizer. Several good ones exist as web apps and as Jupyter widgets. Twenty minutes dragging a state vector around while watching gates apply builds intuition that no amount of reading will. Search for one; they come and go. Tier 2.

On spin-½ and the factor of two

Case Study 1's bug is arithmetic; the reason behind it is physics, and the physics is genuinely strange.

Feynman, The Feynman Lectures on Physics, Volume III, Chapters 5 and 6. The clearest explanation anywhere of why spin-½ systems need $4\pi$ to return to themselves. Available free online. It requires no prior quantum mechanics and it is a pleasure to read. Tier 1.
The "Dirac belt trick" / plate trick. A physical demonstration you can do with a belt or a glass of water: rotating an object through $2\pi$ leaves it tangled with its surroundings, and a second $2\pi$ untangles it. Videos abound. Silly-looking, genuinely illuminating, and it makes the half-angle memorable. Tier 2.

On gate synthesis and decomposition

For Case Study 2, and as background for Chapters 10 and 28.

Barenco et al., "Elementary Gates for Quantum Computation" (1995), Physical Review A 52, 3457. The foundational paper on decomposing arbitrary unitaries into elementary gates. It contains the single-qubit $Z$–$Y$–$Z$ result, the two-qubit constructions, and the multi-controlled gate decompositions that Chapter 19 needs. Dense, and worth the effort — a remarkable amount of practical quantum compilation traces directly to this one paper. Tier 1.
The Qiskit transpiler documentation on the Optimize1qGatesDecomposition and UnitarySynthesis passes. What the library actually does, which is not always what the textbook says. Useful when a decomposition surprises you. Tier 2.

On the hardware side of §3.8

McKay et al., "Efficient Z-Gates for Quantum Computing" (2017), Physical Review A 96, 022330. The paper that established virtual $Z$-gates on superconducting hardware — the reason rz is free. If you want to understand why a phase-reference shift in the classical controller is equivalent to a physical rotation, this is the source. It is also the reason IBM's basis gate set looks the way it does. Tier 1.
Chapter 31 of this book takes the pulse layer seriously, including what an sx pulse physically is. Tier 1.

If you want to go the other direction

Any linear algebra text's chapter on unitary and Hermitian matrices. Sheldon Axler's Linear Algebra Done Right or Gilbert Strang's Introduction to Linear Algebra both cover what you need. You do not need this to continue, and you will find Chapters 22 and 24 easier if you have it. Tier 2 — check current editions.

Where to go next. If one thing: read Nielsen and Chuang §1.3, then come back and reread §3.5. The interference argument lands differently the second time.

If you would rather build than read, go to Chapter 4 — where one qubit becomes two, two amplitudes become four, and the tensor product arrives.