Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence
非阿贝尔任意子增殖的统计力学与对称性:从形变到退相干
Avi Vadali, Robijn Vanhove, Ruben Verresen, Jason Alicea, Pablo Sala
AI总结 通过统计力学模型和蒙特卡洛模拟,研究非阿贝尔任意子增殖导致拓扑序失稳的机制,发现两个非阿贝尔任意子物种的增殖会寄生凝聚共享的阿贝尔融合结果,破坏拓扑序。
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拓扑量子计算依赖于编织非阿贝尔任意子,但要求底层拓扑序在非完美态制备和环境噪声下存活。我们证明,拓扑序对波函数形变和退相干(后者通过综合征分布探测)的不稳定性通常由统计力学模型描述,其对称性自然揭示出破坏性的任意子激发。例如,我们将此框架与蒙特卡洛模拟结合,解决了$D_4$拓扑序在形变和量子通道(增殖多个单独无法凝聚的非阿贝尔任意子物种)下的稳定性问题。我们证明,超过有限阈值后,两个非阿贝尔任意子物种的增殖会寄生凝聚一个共享的阿贝尔任意子融合结果,从而破坏拓扑序。我们的基于对称性的方法将由此产生的平凡相与凝聚所有阿贝尔电荷得到的平凡相明确区分;换言之,平凡相“记住”了哪些任意子凝聚。该框架为基于综合征测量识别非阿贝尔拓扑序最优解码器的相关对称性迈出了第一步。
Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, are generically captured by stat-mech models whose symmetries naturally expose the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of $D_4$ topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that individually are unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome, destroying the topological order. Our symmetry-based approach sharply differentiates the resulting trivial phase from that obtained by condensing all Abelian charges; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order.