I. Error-Correcting Codes

The QEC dictionary (Part X's chapters in table form). Codes by [[n,k,d]] — n physical, k logical, distance d (corrects ⌊(d−1)/2⌋ errors):

3-qubit repetition     [[3,1,1(-ish)]]  bit flips only; the concept demo (Ch. 32)
Shor 9-qubit           [[9,1,3]]        first full code; concatenation of the two
5-qubit (Laflamme)     [[5,1,3]]        smallest possible distance-3; deep code
Steane                 [[7,1,3]]        CSS; classical [7,4,3] Hamming doubled
Surface code (rotated) [[2d²,1,d]]      topological; local check; threshold ~1%;
                                        the industrial choice (Ch. 35, Willow)
Color codes            triangular       CSS, transversal gates; layout-hungry
qLDPC                  [[n,k,d]], k>1   high rate; IBM's bet; decoding race (Ch. 79.2)
Bosonic/cat codes      cavity-level     hardware QEC; Alice&Bob, Ocelot (Ch. 80.4)

Concepts: stabilizer group (abelian Pauli subgroup, −I excluded); syndrome (commutation pattern with generators — tells which subspace, not which state); logical operators (Paulis commuting with all stabilizers — the code's vulnerabilities, string-like for surface codes — hence distance from size); threshold (physical error below which distance wins — the theorem making everything possible); decoders (lookup → MWPM → ML → neural; Ch. 37); logical gates (transversal where possible; lattice surgery + magic states where not — Ch. 79). Key numbers to carry: surface-code threshold ~0.5–1% circuit-level; Λ ≈ 10 per distance step at p≈10⁻³; overhead 2d² per logical; T via distillation ≈ 10³–10⁴ physical per logical op.