Simplest fidelity-estimation method for graph states with depolarizing noise
Simplest fidelity-estimation method for graph states with depolarizing noise
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发表时间：
2023-04
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通讯作者：
Tomonori Tanizawa;Yuki Takeuchi;Shion Yamashika;R. Yoshii;S. Tsuchiya
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作者：
Tomonori Tanizawa;Yuki Takeuchi;Shion Yamashika;R. Yoshii;S. Tsuchiya
图态是用于一些量子信息处理任务的纠缠态，例如基于测量的量子计算和量子计量学。随着实验中实现的图形状态的规模的增加，设计有效的方法来估计理想图形状态和实验实现的实际状态之间的保真度变得更加重要。一般来说，任何有效的保真度估计方法都必须使用多个实验设置，即需要在至少两个测量之间切换。最近，已有研究表明，如果噪声可以模型化为相移误差，那么单次测量就足够了。由于比特翻转误差也应该在几个实验中发生，因此希望将这种最简单的方法扩展到包括相位和比特翻转误差的噪声模型。然而，这似乎不是微不足道的，因为他们的结果强烈地依赖于相位反转误差的性质。通过分析比特翻转误差对图状态稳定器算子的影响，得到了去极化噪声的推广，它是一种主要的噪声模型，包括相位误差和比特翻转误差。我们还对我们最简单的噪声模型内插方法进行了数值评估，该方法在反相噪声和去极化噪声之间进行内插。
Graph states are entangled states useful for several quantum information processing tasks such as measurement-based quantum computation and quantum metrology. As the size of graph states realized in experiments increases, it becomes more essential to devise efficient methods estimating the fidelity between the ideal graph state and an experimentally-realized actual state. Any efficient fidelity-estimation method, in general, must use multiple experimental settings, i.e., needs to switch between at least two measurements. Recently, it has been shown that a single measurement is sufficient if the noise can be modeled as the phase-flip error. Since the bit-flip error should also occur in several experiments, it is desired to extend this simplest method to noise models that include phase and bit-flip errors. However, it seems to be nontrivial because their result strongly depends on properties of the phase-flip error. In this paper, by analyzing effects of the bit-flip error on stabilizer operators of graph states, we achieve the extension to the depolarizing noise, which is a major noise model including phase and bit-flip errors. We also numerically evaluate our simplest method for noise models interpolating between the phase-flip and depolarizing noises.