1. U_φ(x)|0⟩ = |φ(x)⟩；角度 ⊗R_σ(x_i)（n = d，O(1)）；振幅 Σ x_j|j⟩（log₂d，O(d)）；重上传 ∏[W_ℓ(θ)V_ℓ(x)]
2. f(x) = Σ_ω c_ω·e^{iω·x}；R_Z 单门 Ω ⊆ {0,±1}，L 次重上传 Ω ⊆ {0,…,±L}
3. k(x,x′) = |⟨0|U†_φ(x′)U_φ(x)|0⟩|²；R_Y 例 k = cos²(Δ/2)
4. ⟨H⟩ = Σ_j E_j|c_j|² ≥ E₀；1−|⟨E₀|ψ⟩|² ≤ (⟨H⟩−E₀)/(E₁−E₀)
5. H_mol 二次量子化式；a†_j = (∏_{k<j}Z_k)⊗σ⁺_j；H = Σ α_k·P_k，L = O(n⁴)
6. UCCSD 参数 n_o·n_v + C(n_o,2)·C(n_v,2)；HEA 高原 Var[∂⟨H⟩/∂θ] = O(2⁻ⁿ)
7. PSR：∂⟨H⟩/∂θ = ½[⟨H⟩₊ − ⟨H⟩₋]（移位 ±π/2）；m ≥ Var/ε²；m_k ∝ |α_k|σ_k；总测量 O(n⁴/ε²)
8. H_C = Σ(1−Z_iZ_j)/2 = (|E|/2)I − ½ΣZ_iZ_j；CNOT·R_z(φ)·CNOT = e^{−iφZ_iZ_j/2}；门数 O(p(|E|+n))
9. r₁ = 0.6924（3 正则最坏）；绝热 Trotter 误差 O(T³/p²) → r_p → 1；K₃：F = 30/16+(3/4)c−(9/8)c²，c = 1/3 → F_max = 2