论文标题
调查噪声通道对统一T-Designs质量的影响
Investigating the effect of noise channels on the quality of unitary t-designs
论文作者
论文摘要
统一的T设计在量子信息理论中具有多种应用，例如量子数据加密和随机基准测试。但是，T-Designs的实验实现会遇到噪声。在这里，我们研究了噪声通道对单量子T-设计质量的影响。我们研究的噪声通道是钻头翻转，相位翻转，位和相位翻转，相阻尼，振幅阻尼和去极化噪声。我们考虑了两个噪声模型：第一个噪声在T-Design统一操作之前施加了噪声，而第二个具有在单一操作后施加噪声。 We show that the single-qubit 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and 5-designs suggest that a 2t-design is significantly more sensitive to noise than a (2t-1)-design and that, with the exception of amplitude damping, a (2t+1)-design is as sensitive to noise as a 2t-design.数字结果还揭示了整个BLOCH球体对噪声的敏感性的实质性变化。特别是，在作用于纯状态时，T-设计似乎对噪声最敏感，并且对最大混合状态的噪声敏感。对于去极化噪声，我们表明我们的两个噪声模型是等效的，对于其他噪声通道，对于模型获得的数字结果，在单位型后，在单位后反映了噪声通道向去极化通道的转化，这是用2设计在随机基准测试中利用的效果。
Unitary t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomised benchmarking. However, experimental realisations of t-designs are subject to noise. Here we investigate the effect of noise channels on the quality of single-qubit t-designs. The noise channels we study are bit flips, phase flips, bit and phase flips, phase damping, amplitude damping, and depolarising noise. We consider two noise models: the first has noise applied before the t-design unitary operations, while the second has noise applied after the unitary operations. We show that the single-qubit 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and 5-designs suggest that a 2t-design is significantly more sensitive to noise than a (2t-1)-design and that, with the exception of amplitude damping, a (2t+1)-design is as sensitive to noise as a 2t-design. Numeric results also reveal substantial variations in sensitivity to noise throughout the Bloch sphere. In particular, t-designs appear to be most sensitive to noise when acting on pure states and least sensitive to noise for the maximally mixed state. For depolarising noise, we show that our two noise models are equivalent, and for the other noise channels, numeric results obtained for the model where noise is applied after the unitaries reflect the transformation of the noise channel into a depolarising channel, an effect exploited in randomised benchmarking with 2-designs.
