An Upper Bound on the Threshold Quantum Decoherence Rate

Abstract

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 $\le 2$ 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 ${\eta }_0\ge 10^{-6}-10^{-4}$, whereas the only upper bound known before is ${\eta }_0\le 0.74$. In this note we improve the latter bound to ${\eta }_0\le 1/2$, under the assumption $QP⊈QN{C}^1$. 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 ${\eta }_0\le 1-1/k$.

9 pages