论文标题
来自量子相估计的Hermitian矩阵确定性
Hermitian Matrix Definiteness from Quantum Phase Estimation
论文作者
论文摘要
提出了一种按照其签名（正半准，负或无限）对一般遗产基质进行分类的算法。它建立在量子相估计算法上，该算法存储一个辅助量子量子器中遗传基质的特征值的符号。矩阵的签名是从此单个辅助量子量子中的自旋算子的平均值中提取的。该算法是概率的，但表现出良好的性能，可实现97％的正确分类，几乎没有量子位。在通用矩阵的情况下，计算成本量表与经典的成本量表相当，但是对于$ k $ - $ - 局部或稀疏的汉密尔顿人（例如$ k $ a）的矩阵类别有了显着改善。
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a Hermitian matrix in one ancillary qubit. The signature of the matrix is extracted from the mean value of a spin operator in this single ancillary qubit. The algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits. The computational cost scales comparably to the classical one in the case of a generic matrix, but improves significantly for restricted classes of matrices like $k$-local or sparse hamiltonians.
