An upper bound on the threshold quantum decoherence rate (pp222-228)
        A.A. Razborov
          doi: https://doi.org/10.26421/QIC4.3-7
Abstracts: Let $\eta_0$ be the supremum of those $\eta$ for which every poly-size quantum circuit can be simulated by another poly-size quantum circuit with gates of fan-in $\leq 2$ that tolerates random noise independently occurring on all wires at the constant rate $\eta$. Recent fundamental results showing the principal fact $\eta_0>0$ give estimates like $\eta_0\geq 10^{-6}\mbox{--}10^{-4}$, whereas the only upper bound known before is $\eta_0\leq 0.74$.}{In this note we improve the latter bound to $\eta_0\leq 1/2$, under the assumption ${\bf QP}\not\subseteq {\bf QNC^1}$. More generally, we show that if the decoherence rate $\eta$ is greater than 1/2, then we can not even store a single qubit for more than logarithmic time. Our bound also generalizes to the simulating circuits allowing gates of any (constant) fan-in $k$, in which case we have $\eta_0\leq 1-\frac 1k$.
Key words: fault-tolerant quantum computation, noise rate