如何在ZXW演算中对哈密顿量求和与求指数
How to Sum and Exponentiate Hamiltonians in ZXW Calculus
AI总结：
本文在ZXW演算中开发求和与求指数技术，以图解方式处理量子哈密顿量，支持薛定谔方程线性性证明及哈密顿量模拟，为量子化学和凝聚态物理提供新框架。
摘要：
本文开发了ZXW演算中的实用求和技巧，用于推理量子动力学，如酉时间演化。首先，我们给出了ZXW演算中一大类线性算子和的直接表示，包括任意量子比特哈密顿量。作为应用，我们证明了薛定谔方程的线性性，并给出了Greene-Diniz等人哈密顿量的图解表示，该论文是首个使用量子计算模拟碳捕获的论文。然后，我们利用Cayley-Hamilton定理，原则上展示了如何在ZXW演算中对任意量子比特哈密顿量求指数。最后，我们开发了实用技术，并展示了如何以图解方式进行泰勒展开和Trotter化以用于哈密顿量模拟。这为使用ZXW演算解决量子化学和凝聚态物理中的问题建立了框架。
英文摘要：
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.
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