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arXiv 2403.04767quant-phcond-mat.dis-nncond-mat.stat-mechcond-mat.str-el
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表面码的鲁棒隐形传态与拓扑量子相变级联

Robust teleportation of a surface code and cascade of topological quantum phase transitions

Finn Eckstein, Bo Han, Simon Trebst, Guo-Yi Zhu

备注：
7 + 5 pages; 5 + 3 figures
发表信息：
PRX Quantum 5, 040313 (2024)
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AI总结：

本文提出用基本 Bell 测量隐形传态表面码态的鲁棒协议，将相干误差阈值映射为含 Nishimori 无序的 Ashkin–Teller 相变问题，并发现自对偶线上阈值发散。

摘要：

隐形传态是量子测量在量子物理学中充当强大资源的一个方面，因为局域测量允许以非局域方式引导量子信息。尽管这一点对于单个 Bell 对早已确立，但使用非最大纠缠资源对多量子比特纠缠态进行隐形传态，提出了一种根本不同的挑战。在此，我们研究一种具体可实现的协议，利用基本 Bell 测量隐形传态一个长程纠缠的表面码态，并考察其在削弱 Bell 纠缠的相干误差存在时的稳定性。我们将底层阈值问题与弱测量下任意子凝聚的物理联系起来，并将其映射到统计力学中具有 Nishimori 型无序的 Ashkin–Teller 模型的一个变体，该模型会产生相变级联。通过调节局域 Bell 测量的角度，我们发现阈值连续变化。值得注意的是，沿自对偶线，在 $X+Z$ 角度处阈值趋于无穷大——这表明在隐形传态一个自对偶拓扑表面码时，无限弱的纠缠就已足够。我们的隐形传态协议可在动态可配置的 Rydberg 原子阵列中直接实现，从而为实际展示量子测量的能力提供指导。

英文摘要：

Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow to steer quantum information in a non-local way. While this has long been established for a single Bell pair, the teleportation of a many-qubit entangled state using non-maximally entangled resources presents a fundamentally different challenge. Here we investigate a tangible protocol for teleporting a long-range entangled surface code state using elementary Bell measurements and its stability in the presence of coherent errors that weaken the Bell entanglement. We relate the underlying threshold problem to the physics of anyon condensation under weak measurements and map it to a variant of the Ashkin-Teller model of statistical mechanics with Nishimori type disorder, which gives rise to a cascade of phase transitions. Tuning the angle of the local Bell measurements, we find a continuously varying threshold. Notably, the threshold moves to infinity for the $X+Z$ angle along the self-dual line -- indicating that infinitesimally weak entanglement is sufficient in teleporting a self-dual topological surface code. Our teleportation protocol, which can be readily implemented in dynamically configurable Rydberg atom arrays, thereby gives guidance for a practical demonstration of the power of quantum measurements.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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