论文标题
基于块编码的量子放松行和列迭代方法
Quantum relaxed row and column iteration methods based on block-encoding
论文作者
论文摘要
迭代方法通常用于求解方程的线性系统。我们通过在迭代过程中构造单位矩阵来介绍放松的行和列迭代方法的量子算法，该过程概括了行和列迭代方法以在量子计算机上求解线性系统。与常规的行和列迭代方法相比，选择适当的参数时，收敛会加速。一旦量子状态有效制备，我们放松的行和色谱柱方法的复杂性将呈指数改善，并与迭代步骤的数量线性线性。此外，在这些算法中不需要阶段估计和哈密顿模拟。
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and column iteration methods to solve linear systems on a quantum computer. Comparing with the conventional row and column iteration methods, the convergence accelerates when appropriate parameters are chosen. Once the quantum states are efficiently prepared, the complexity of our relaxed row and column methods is improved exponentially and is linear with the number of the iteration steps. In addition, phase estimations and Hamiltonian simulations are not required in these algorithms.
