论文标题
Riemannian几何形状和自动分化，以优化量子物理和量子技术问题
Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
论文作者
论文摘要
用约束的优化是量子物理和量子信息科学中的一个典型问题，对于高维系统和复杂体系结构（例如张量网络）而言，这变得尤其具有挑战性。在这里，我们使用Riemannian几何形状的思想对单一和等距矩阵的流形以及正定矩阵的锥进行优化。将这种方法与自动差异的最新计算方法相结合，我们证明了riemannian优化在对低能频谱和多方汉密尔顿多部分哈密顿量的低能频谱和本征态的研究中的功效量子门的计算，分解和量子状态的断层扫描。开发方法的通用性以及提供的开源软件使人们能够将Riemannian优化应用于复杂的量子体系结构，远远超出了列出的问题，例如对嘈杂量子系统的最佳控制。
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of Riemannian geometry to perform optimization on manifolds of unitary and isometric matrices as well as the cone of positive-definite matrices. Combining this approach with the up-to-date computational methods of automatic differentiation, we demonstrate the efficacy of the Riemannian optimization in the study of the low-energy spectrum and eigenstates of multipartite Hamiltonians, variational search of a tensor network in the form of the multiscale entanglement-renormalization ansatz, preparation of arbitrary states (including highly entangled ones) in the circuit implementation of quantum computation, decomposition of quantum gates, and tomography of quantum states. Universality of the developed approach together with the provided open source software enable one to apply the Riemannian optimization to complex quantum architectures well beyond the listed problems, for instance, to the optimal control of noisy quantum systems.
