BQP for promise problems in the fixed QC14 model

A promise problem $\mathrm{\Pi }=(Y,N)$ belongs to BQP in the QC14 model when there exist a full-list uniform family $(C_n)$ and a polynomial-time acceptance predicate $A_n$ as in Full-list uniform quantum circuit family and Quantum acceptance probability for a finite promise computation such that, for every $x\in Y$, $p_{C_{\mathrm{\mid }x\mathrm{\mid }}}(x)\ge \frac{2}{3},$ and for every $x\in N$, $p_{C_{\mathrm{\mid }x\mathrm{\mid }}}(x)\le \frac{1}{3}\mathrm{.}$ By The partial-output acceptance law is a finite probability law, $p_{C_n}(x)$ is the probability of the specified acceptance event and lies in $[0,1]$. No condition is imposed for $x\mathrm{\notin }Y\cup N$ (Promise problem). The gate alphabet is exactly $H,T,T^{†},\mathrm{C}\mathrm{N}\mathrm{O}\mathrm{T}$; its matrix entries lie in $\mathbb{Q}({\zeta }_8)=\mathbb{Q}(i,\sqrt{2})$ as specified by Full-list uniform quantum circuit family. This definition does not assert a BQP-versus-classical separation, nor does it assert an unproved equivalence with another circuit-uniformity convention.