1. 定义：‖A − α(⟨0|^{⊗m}⊗I)U_A(|0⟩^{⊗m}⊗I)‖ ≤ ε；推论 ‖A‖ ≤ α + ε
2. LCU：λ = Σ_k|α_k|、m_a = ⌈log₂L⌉、PREP|0⟩ = (1/√λ)Σ√|α_k||k⟩、SELECT = Σ|k⟩⟨k|⊗sgn(α_k)U_k
3. 左上块 = A/λ（精确 (λ, m_a, 0)-编码）；门数 O(L·C_U + poly(m_a))
4. Pauli：λ = Σ_P|α_P|；C_{U_A} = O(L·n + poly(m_a))
5. 对角：U_A = Σ_j|j⟩⟨j|⊗R_y(2·arccos(d_j/α))，m_a = 1
6. 乘积：(α_Aα_B, m_A+m_B, α_Bε_A + α_Aε_B + ε_Aε_B)——需独立寄存器
7. 线性组合：(|c|α_A + |d|α_B, 1+m_A+m_B, |c|ε_A + |d|ε_B)；a₀ = cα_A/(|c|α_A+|d|α_B)、a_1 = dα_B/(|c|α_A+|d|α_B)
8. QSVT 次数：A⁻¹ O(κ·log(κ/ε))；e^{−iAt} O(t + log(1/ε))；e^{−βA} O(β + log(1/ε))；阈值 O((1/τ)·log(1/ε))