What does this equation mean?

The reason NISQ-era hardware imposes such a hard ceiling on quantum machine learning specifically is a simple compounding effect. If a device executes a circuit of N sequential gates, each with per-gate fidelity 1-$\varepsilon$ , and errors accumulate independently, the probability the whole circuit runs without error falls off as $F_{\text{circuit}} \approx (1-\varepsilon)^N$. which decays exponentially in circuit depth for any fixed error rate $\varepsilon$ > 0 . This is precisely the noise floor Preskill’s paper is about, and it is why serious NISQ-era quantum machine learning proposals are built around short, shallow circuits matched to a specific problem rather than long, general-purpose programs — the strategy quantum computing borrowed, whether its practitioners framed it this way or not, from the same lesson optical computing learned two decades earlier: work within what the noisy substrate actually does well, rather than against it.