论文标题
部分可观测时空混沌系统的无模型预测
Complexity of frustration: a new source of non-local non-stabilizerness
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。
We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic" (measured as the Stabilizer Rényi Entropy -SRE-) that grows logarithmic with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with an extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classic point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state's SRE is the sum of that of the $W$-states plus an extensive local contribution. Our work reveals that $W$-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.
