论文标题
与局部去极化噪声的经典模拟量子电路
Classically Simulating Quantum Circuits with Local Depolarizing Noise
论文作者
论文摘要
我们研究了噪声对由计算典型（CT）状态定义的量子电路的经典模拟性和有效计算的稀疏（EC）操作的影响。我们称之为CT-ECS电路的此类电路的示例是IQP，Clifford Magic和Clifford Circuits。这意味着存在各种CT-ECS电路，使它们的输出概率分布是抗浓缩的，并且在无噪声设置（在合理的假设下）中不经典模拟。首先，我们考虑一个噪声模型，其中在计算结束时将具有任意恒定速率的去极化通道应用于每个量子。我们表明，在此噪声模型下，如果已知噪声速率的近似值，则可以在经典上模拟具有抗浓缩输出概率分布的任何CT-ECS电路。这表明小噪声的存在极大地影响了CT-ECS电路的经典模拟性。然后，我们考虑噪声模型的扩展，其中噪声速率可以随着每个量子的变化而变化，并为具有抗分解输出概率分布的经典模拟CT-ECS电路提供了相似的足够条件。
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions.
