论文标题
矩阵操作和方程线性系统的量子算法
Quantum algorithms for matrix operations and linear systems of equations
论文作者
论文摘要
基本矩阵操作和方程式线性系统在科学研究中无处不在。使用“发送者接收器”模型，我们提出了用于基质操作的量子算法，例如矩阵矢量产物，矩阵矩阵乘积，两个矩阵的总和以及计算矩阵的确定性和倒数。我们将矩阵条目编码为发件人纯初始状态的概率幅度。将适当的统一转换应用于完整的量子系统后，可以在接收器密度矩阵的某些块中找到所需的结果。这些量子方案可以用作其他量子方案的子例程。此外，我们提出了一种用于求解方程线性系统的替代量子算法。
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product, matrix-matrix product, the sum of two matrices, and calculation of determinant and inverse of a matrix. We encode the matrix entries into the probability amplitudes of pure initial states of senders. After applying a proper unitary transformation to the complete quantum system, the desired result can be found in certain blocks of the receiver's density matrix. These quantum protocols can be used as subroutines in other quantum schemes. Furthermore, we present an alternative quantum algorithm for solving linear systems of equations.
