ZQP on promise problems with bounded failure

In this page, $\mathrm{Z}\mathrm{Q}\mathrm{P}$ denotes the following bounded-failure zero-error promise class. A promise problem $\mathrm{\Pi }=(Y,N)$ belongs to $\mathrm{Z}\mathrm{Q}\mathrm{P}$ if there are a full-list uniform QC14 family $(C_n)$, a polynomial-time total label decoder $D_n(x,z)\in \{\mathrm{Y}\mathrm{E}\mathrm{S},\mathrm{N}\mathrm{O},?\}$, and the finite output law of Finite quantum promise-computation model, Full-list uniform quantum circuit family, and Quantum acceptance probability for a finite promise computation, such that for every $x\in Y$ the probability of $\mathrm{Y}\mathrm{E}\mathrm{S}$ is at least $2\mathrm{/}3$ and the probability of $\mathrm{N}\mathrm{O}$ is zero, while for every $x\in N$ the probability of $\mathrm{N}\mathrm{O}$ is at least $2\mathrm{/}3$ and the probability of $\mathrm{Y}\mathrm{E}\mathrm{S}$ is zero. All output strings receive one of the three labels, so the remaining probability is the allowed failure label $?$; the output law is normalized by The partial-output acceptance law is a finite probability law. No promise condition is imposed off $Y\cup N$.

This explicit fixed-circuit, bounded-failure convention is sufficient for the containments proved on this page. No equivalence with an expected-time quantum zero-error model or with $\mathrm{B}\mathrm{Q}\mathrm{P}\cap \mathrm{c}\mathrm{o}\mathrm{B}\mathrm{Q}\mathrm{P}$ is asserted.