论文标题
量子炼金术和通用正交性灾难
Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
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。
Many-particle quantum systems with intermediate anyonic exchange statistics are supported in one spatial dimension. In this context, the anyon-anyon mapping is recast as a continuous transformation that generates shifts of the statistical parameter $κ$. We characterize the geometry of quantum states associated with different values of $κ$, i.e., different quantum statistics. While states in the bosonic and fermionic subspaces are always orthogonal, overlaps between anyonic states are generally finite and exhibit a universal form of the orthogonality catastrophe governed by a fundamental statistical factor, independent of the microscopic Hamiltonian. We characterize this decay using quantum speed limits on the flow of $κ$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
