H. Quantum Channels

Noise, formalized (Ch. 29–31's dictionary). A channel ℰ is a completely-positive trace-preserving map; three equivalent pictures: Kraus ℰ(ρ) = Σₖ KₖρKₖ† (ΣK†ₖKₖ=I) — the implementation view; Stinespring ℰ(ρ) = tr_E[V ρ V†] — the physics view (unitary on a bigger system, discard environment — noise is entanglement leakage, Ch. 2.12); Chi/χ process matrix — the tomography view. The canon, with Kraus structure:

Bit flip p:        {√(1−p)I, √p X}
Phase flip p:      {√(1−p)I, √p Z}
Depolarizing p:    p ρ → I/2 mixtures; Kraus {√(1−3p/4)I, √(p/4)X, √(p/4)Y, √(p/4)Z}
Amplitude damping: {K₀=[[1,0],[0,√(1−γ)]], K₁=[[0,√γ],[0,0]]}  T1 physics; not unital
Phase damping/dephasing: diagonal decay of off-diagonals; T2 physics
Readout error:     classical confusion matrix per qubit (not Kraus on ρ; post-processing)

Key properties: unital (ℰ(I)∝I) vs. non-unital (amplitude damping relaxes toward |0⟩); composition = concatenating noise; channel fidelity measures worst/best state survival. Estimation: randomized benchmarking (Ch. 31) estimates gate-channel quality without process tomography's exponential cost. In code (Ch. 68's project): apply_channel with Kraus sampling, verified against density-matrix evolution.