| （英） |
Quantum eigenvalue/singular-value transformation (QET/QSVT) has attracted much interest as grand
uni cation of quantum algorithms, which uni es and improves various famous quantum algorithms such as Grover's search and Hamiltonian simulation. However, in order to execute QET/QSVT for large quantum systems, we usually su er from numerical instability in determining the parameter set for it. In our study, we propose recursive QET/QSVT as a potential algorithm that can partially resolve this instability. The recursive QET/QSVT recursively organize QET/QSVT with simple matrix polynomials and obtain complicated matrix polynomials after the iteration, which allows the coexistence of numerical stability and complicated quantum tasks. In particular, we show that the recursive QET/QSVT enables us to construct matrix sign functions, which is useful for eigenstate filtering, based on Newton iteration without suffering from the instability at all. |