Jinpeng Liu, Assistant Professor, Tsinghua University

Weiying Zheng, Professor

Quantum for Science: Efficient Quantum Algorithms for Linear and Nonlinear Dynamics

10:00-11:00 August 8 (Thursday), N202

Fault-tolerant quantum computers are expected to excel in simulating unitary dynamics, such as the dynamics of a quantum state under a Hamiltonian. Most applications in scientific and engineering computations involve non-unitary and/or nonlinear dynamics. Therefore, efficient quantum algorithms are the key for unlocking the full potential of quantum computers to achieve comparable speedup in these general tasks.

First, we propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. The LCHS method can achieve optimal cost in terms of state preparation [1]. Second, we give the first efficient (polynomial time) quantum algorithm for nonlinear differential equations with sufficiently strong dissipation. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in the evolution time [2]. Our work shows that fault-tolerant quantum computing can potentially address complex non-unitary and nonlinear phenomena in natural and data sciences with provable efficiency [3].

References:

[1] Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost. Physical Review Letters, 131(15):150603 (2023)  .

[2] Efficient quantum algorithm for dissipative nonlinear differential equations. Proceedings of the National Academy of Science 118, 35 (2021).

[3] Towards provably efficient quantum algorithms for large-scale machine learning models. Nature Communications 15, 434 (2024)

报告人简介：刘锦鹏，清华大学数学科学中心助理教授（2024年秋入职），2022-2024年在麻省理工和伯克利任博士后，2022年博士毕业于马里兰大学，2017年本科毕业于北航-中科院华罗庚班。本人研究方向为量子科学计算与量子科学智能，发表PNAS、Nat.Commun. 、PRL、CMP、JCP、Quantum等期刊和NeurIPS、QIP、TQC等会议，受到Quanta、SIAM News、MATH+等科技媒体报道，曾获ICCM毕业论文奖 (博士论文金奖)、James C. Alexander Prize、QISE-NET Award等，作为co-PI主持美国NSF一项种子基金，担任量子信息权威期刊Quantum（JCR Q1，IF 6.4）的编委（中国高校仅3人）。