Quantum singular value transformation (QSVT) is a unifying framework that encapsulates most known quantum algorithms. However, existing implementations rely on block encoding, incurring an intrinsic O(log L) ancilla overhead when there are L terms. In this talk, I will introduce some methods for implementing QSVT without block encodings, based on our recent work [arXiv:2504.02385] and [arXiv:2510.06851]. We propose algorithms that achieve near-optimal complexity using only a single ancilla qubit. One approach utilizes Trotter and Richardson extrapolation. We apply our framework to two fundamental tasks: solving quantum linear systems and estimating ground-state properties of Hamiltonians, obtaining polynomial advantages over prior randomized algorithms. Finally, we benchmark our ground-state property estimation algorithm on electronic structure Hamiltonians and the transverse-field Ising model with long-range interactions. In both cases, our approach outperforms prior work by several orders of magnitude in circuit depth, establishing our framework as a practical and resource-efficient alternative for early fault-tolerant quantum devices.

报告人简介：李彤阳，北京大学前沿计算研究中心研究员、博雅青年学者，国家自然科学基金面上项目、重大研究计划培育项目负责人。他的科研围绕量子计算、人工智能、理论计算机的交叉领域展开，研究成果已在Nature Physics、Nature Communications、Journal of the ACM、Physical Review Letters、IEEE Transactions on Information Theory、STOC、ICML、NeurIPS、ICLR 等期刊、会议发表论文四十余篇。