① $y_{\mathrm{pred}} = \langle 0|U^\dagger(x,\theta) \cdot M \cdot U(x,\theta)|0\rangle$(QNN 前馈)
② $\partial\langle M\rangle/\partial\theta_k = (1/2)(\langle M\rangle_+ - \langle M\rangle_-)$,采样点 $\theta_k \pm \pi/2$(参数平移)
③ $\mathrm{Pr}(0^n) = |\langle\phi(x)|\phi(x')\rangle|^2$(碰撞测量);采样 $O(\log(1/\delta)/\epsilon^2)$
④ $f_\theta(x) = \langle\phi'(x)| \cdot M \cdot |\phi'(x)\rangle$,$|\phi'(x)\rangle = U_\phi(x) \cdot W|0\rangle$(QNN = 核模型)
⑤ $\mathrm{Var}[\partial C/\partial\theta_j] \sim 2^{-n}$(高原定义);2-设计界 $\mathrm{Var} \lesssim \mathrm{poly}(n)/4^n$
⑥ $C_L \le C_G \le n \cdot C_L$;$\mathrm{Var}[\partial C_L] \sim 1/\mathrm{poly}(n)$(局部代价)
⑦ $\mathrm{Var} \lesssim \eta^{2L} \cdot \mathrm{Var}_0 + O((1 - \eta^L)^2/2^n)$,$\eta = e^{-\epsilon}$(噪声高原)
⑧ $E[|\langle\psi|\phi\rangle|^2] = 2^{-n}$(集中测度统一式)