标题： 无序电子的量子线性代数 显示英文标题

标题： Quantum linear algebra for disordered electrons

摘要： 我们描述了如何利用量子线性代数来模拟一个物理上现实的无序非相互作用电子模型。 一维以外的无序电子的物理特性由于Anderson局域化转变的关键性质或者大局域长度的存在，挑战了经典计算的能力，而局域态密度的非典型分布限制了无序平均方法的能力。 从无序非相互作用哈密顿量的块状编码开始，我们描述了如何使用量子奇异值变换、量子幅值估计和迹估计来模拟关键的物理量，包括约简密度矩阵、格林函数和局域态密度，以及诸如电导率等整体平均可观测量。 我们进一步讨论了一种量子优势，这种优势随着系统大小呈多项式增长，并且随着晶格维度呈指数增长。 显示英文摘要

摘要： We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons. The physics of disordered electrons outside of one dimension challenges classical computation due to the critical nature of the Anderson localization transition or the presence of large localization lengths, while the atypical distribution of the local density of states limits the power of disorder averaged approaches. Starting from the block-encoding of a disordered non-interacting Hamiltonian, we describe how to simulate key physical quantities, including the reduced density matrix, Green's function, and local density of states, as well as bulk-averaged observables such as the linear conductivity, using the quantum singular value transformation, quantum amplitude estimation, and trace estimation. We further discuss a quantum advantage that scales polynomially with system size and exponentially with lattice dimension.