论文标题
如何在ZXW微积分中概括和指定哈密顿人
How to Sum and Exponentiate Hamiltonians in ZXW Calculus
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。
This paper develops practical summation techniques in ZXW calculus to reason about quantum dynamics, such as unitary time evolution. First we give a direct representation of a wide class of sums of linear operators, including arbitrary qubits Hamiltonians, in ZXW calculus. As an application, we demonstrate the linearity of the Schroedinger equation and give a diagrammatic representation of the Hamiltonian in Greene-Diniz et al, which is the first paper that models carbon capture using quantum computing. We then use the Cayley-Hamilton theorem to show in principle how to exponentiate arbitrary qubits Hamiltonians in ZXW calculus. Finally, we develop practical techniques and show how to do Taylor expansion and Trotterization diagrammatically for Hamiltonian simulation. This sets up the framework for using ZXW calculus to the problems in quantum chemistry and condensed matter physics.
