Quantum Algorithms based on the Block-Encoding Framework for Matrix Functions by Contour Integrals

Understand

The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula.

• In this paper, we show a concrete construction of a framework to implement the linear combination of the inverses on quantum computers and propose a quantum algorithm for matrix functions based on the framework.
• Compared with the previous study [S.
• Takahira, A.