主持人：郑海标
报告简介：We present a quantum computational framework for solving linear algebra systems arising from iterative solvers. The framework combines the Schr?dingerization technique [S. Jin, N. Liu, and Y. Yu, Phys. Rev. Lett. 133, 230602 (2024)] with preconditioning strategies to achieve near-optimal complexity. Schr?dingerization transforms linear differential equations into Schrodinger-type systems with unitary evolution in a higher dimension, making them suitable for quantum computation. In particular, the BPX preconditioner is integrated with Schr?dingerization to obtain near-optimal complexity for elliptic problems. Building on this, we extend the method to the Helmholtz equation, incorporating dispersion correction and tailored preconditioning to efficiently address indefiniteness. These results show that quantum preconditioning provides a scalable pathway from well-conditioned systems to challenging wave problems.