An upper bound on the threshold quantum decoherence rate
An upper bound on the threshold quantum decoherence rate
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发表时间：
2003-10
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通讯作者：
A. Razborov
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作者：
A. Razborov
设η0是那些η的上确界，对于这些上确界，每个多尺寸量子电路可以由另一个具有扇入≤ 2的门的多尺寸量子电路来模拟，该多尺寸量子电路以恒定速率η容忍在所有线路上独立发生的随机噪声。最近的基本结果表明，主要事实η0 > 0给出了估计，如η0 ≥ 10-6 - 10-4，而之前唯一已知的上限是η0 ≤ 0.74。在本文中，我们在假设QP <$QNC 1的条件下，将后一个界改进为η0 ≤ 1/2。更一般地说，我们证明了如果退相干率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。我们的界也推广到允许任意（常数）扇入k的门的模拟电路，在这种情况下，我们有η0 ≤ 1 - 1/k。
Let η0 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 ≤ 2 that tolorates random noise independently occurring on all wires at the constant rate η. Recent fundamental results showing the principal fact η0 > 0 give estimates like η0 ≥ 10-6 - 10-4, whereas the only upper bound known before is η0 ≤ 0.74. In this note we improve the latter bound to η0 ≤ 1/2, under the assumption QP ⊆ QNC1. More generally, we show that if the decohereace 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 η0 ≤ 1 - 1/k.