Oscillator-to-Oscillator Codes Do Not Have a Threshold
Oscillator-to-Oscillator Codes Do Not Have a Threshold
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振荡器到振荡器代码没有阈值
DOI：
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发表时间：
2021
影响因子：
2.5
通讯作者：
Robert Koenig
中科院分区：
文献类型：
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作者：
Lisa Hänggli;Robert Koenig
已知的是，仅使用高斯状态和操作不能保护连续变量量子信息免受自然发生的噪声的影响。Noh等人提出了依赖于非高斯资源状态的玻色子振荡器到振荡器编码作为替代方案，并表明这些编码可以导致逻辑水平上的有效错误强度的降低，如通过经典位移噪声信道的方差所测量的。振荡器到振荡器码通过高斯N模幺正态和N-K个辅助单模Gottesman-Kitaev-Pressure-state将K个逻辑玻色子模（在任意状态下）嵌入到N个物理模中。在这里，我们要问-类似于量子比特纠错码-是否存在具有以下阈值性质的振荡器到振荡器码族：它们允许将方差低于某个阈值的物理位移噪声转换为方差上限为任何（任意）常数的逻辑噪声。我们发现，这是不是这样的情况下，如果编码酉涉及一个常数量的压缩和最大似然误差解码使用。我们给出了逻辑错误概率的一般下界，它只是压缩量的函数，与模的数目无关。因此，与最大似然误差解码相结合的任何物理上可实现的振荡器到振荡器码族不允许阈值。
It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only. Noh et al. proposed bosonic oscillator-to-oscillator codes relying on non-Gaussian resource states as an alternative, and showed that these encodings can lead to a reduction of the effective error strength at the logical level as measured by the variance of the classical displacement noise channel. An oscillator-to-oscillator code embeds K logical bosonic modes (in an arbitrary state) into N physical modes by means of a Gaussian N-mode unitary and N-K auxiliary one-mode Gottesman-Kitaev-Preskill-states. Here we ask if – in analogy to qubit error-correcting codes – there are families of oscillator-to-oscillator codes with the following threshold property: They allow to convert physical displacement noise with variance below some threshold value to logical noise with variance upper bounded by any (arbitrary) constant. We find that this is not the case if encoding unitaries involving a constant amount of squeezing and maximum likelihood error decoding are used. We show a general lower bound on the logical error probability which is only a function of the amount of squeezing and independent of the number of modes. As a consequence, any physically implementable family of oscillator-to-oscillator codes combined with maximum likelihood error decoding does not admit a threshold.
影响因子：
2.9
作者：
Christophe Vuillot;H. Asasi;Yang Wang;L. Pryadko;B. Terhal
通讯作者：
Christophe Vuillot;H. Asasi;Yang Wang;L. Pryadko;B. Terhal