Topological Contextuality and Anyonic Statistics of Photonic-Encoded Parafermions
Topological Contextuality and Anyonic Statistics of Photonic-Encoded Parafermions
复制标题
光子编码平费米子的拓扑上下文和任意统计
DOI：
10.1103/prxquantum.2.030323
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发表时间：
2021-08-09
期刊：
影响因子：
9.7
通讯作者：
Guo, Guang-Can
中科院分区：
文献类型：
--
作者：
Liu, Zheng-Hao;Sun, Kai;Guo, Guang-Can
预计在马约拉纳零模态测量过程中会出现准粒子中毒，这为实现基于马约拉纳的量子计算提出了一个基本问题。类费米子是马约拉纳费米子的自然推广，可以编码对准粒子中毒免疫的拓扑量子。虽然预计超导分数量子霍尔系统中会出现对费米子，但目前的技术还无法实现。为了绕过这个问题，我们采用光子量子模拟器来实验演示基于平子费子的通用量子计算的关键组件。我们在本文中的贡献是双重的。首先，通过操纵光子态，我们实现了与平费米子的编织统计相对应的克利福德算子贝里相。其次，我们通过展示对费米子编码的量子态的上下文关系，首次研究了拓扑系统中的量子上下文关系。重要的是，我们发现拓扑编码的上下文打开了神奇状态蒸馏的道路，而上下文和编织诱导的克利福德门都对局部噪声具有弹性。通过引入上下文，我们的光子量子模拟为实现拓扑量子计算的物理稳健方法迈出了第一步。
Quasiparticle poisoning, expected to arise during the measurement of the Majorana zero-mode state, poses a fundamental problem for the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can encode topological qudits immune to quasiparticle poisoning. While parafermions are expected to emerge in superconducting fractional quantum Hall systems, they are not yet attainable with current technology. To bypass this problem, we employ a photonic quantum simulator to experimentally demonstrate the key components of parafermion-based universal quantum computation. Our contributions in this paper are twofold. First, by manipulating the photonic states, we realize Clifford-operator Berry phases that correspond to braiding statistics of parafermions. Second, we investigate the quantum contextuality in a topological system for the first time by demonstrating the contextuality of parafermion-encoded qudit states. Importantly, we find that the topologically encoded contextuality opens the way to magic state distillation, while both the contextuality and the braiding-induced Clifford gates are resilient against local noise. By introducing contextuality, our photonic quantum simulation provides the first step toward a physically robust methodology for realizing topological quantum computation.