论文标题
拓扑表征,扭曲,凝结和反射
Topological Characterization with a Twist, Condensation, and Reflection
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they are utilized in quantum algorithms. We contribute to this grand challenge by providing a series of experimentally accessible near- and medium-term protocols assessing the fidelity of logical processes. To do so we examine logical operators and anyonic quasiparticle excitations in twisted $\mathbb{Z}_{N=2,4}$ gauge theories. Extending the finite twist, a promising route to Ising computing in its own right, to a non-contractible twist fuses prior logical operators together and results in a twisted qubit code. The code is notable for a doubled and tripled code distance for logical $Y$ and $X$ errors respectively. Next, we review the deconfinement properties of a $\mathbb{Z}_4$ double semion condensation and provide an error correction algorithm. Based on this understanding we then present a $\mathbb{Z}_4$ topological quasiparticle reflectometry and scattering protocol. The protocol infers the topological properties of the system and serves as a high-level metric for the performance and lifetime of the interfaced topological codes. Our logical and scattering protocols are suitable for near-term devices where many physical qubits encode few logical qubits. The topological lifetime of a particle within a condensate conjugacy class, previously considered in fabricated and hetero-structured condensed-matter experiments, serves as a unifying performance metric across synthetic, qubit-based, and naturally occurring topological order.