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arXiv quant-ph/0310136quant-ph
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阈值量子退相干率的上界

An Upper Bound on the Threshold Quantum Decoherence Rate

Alexander A. Razborov

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9 pages
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摘要：

令$η_0$是那些$η$的上确界，对于这些$η$，每个多尺寸量子电路可以由具有扇入$\leq 2$的门的另一个多尺寸量子电路来模拟，该扇入$η$容忍以恒定速率独立地出现在所有导线上的随机噪声。最近的基本结果显示的主要事实$η_0>0$给估计像$η_0\geq 10^{-6}-10^{-4}$，而唯一的上限已知之前是$η_0\leq 0.74$。本文在假设$QP\not\subseteq QNC^1$的条件下，将后一个界改进为$η_0\leq 1/2$.更一般地说，我们表明，如果退相干率$η$大于1/2，那么我们甚至不能存储一个量子比特超过对数时间。我们的界限也推广到允许任何（恒定）扇入$k$的门的模拟电路，在这种情况下，我们有$η_0\leq 1-1/k$。

英文摘要：

Let $η_0$ be the supremum of those $η$ 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 $η$. Recent fundamental results showing the principal fact $η_0>0$ give estimates like $η_0\geq 10^{-6}-10^{-4}$, whereas the only upper bound known before is $η_0\leq 0.74$. In this note we improve the latter bound to $η_0\leq 1/2$, under the assumption $QP\not\subseteq QNC^1$. More generally, we show that if the decoherence rate $η$ 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 $η_0\leq 1-1/k$.

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