报告题目：Quantum algorithms for partial differential equations (updates!)

报告人：Prof. Nana Liu（Shanghai Jiao Tong University）

报告时间：2024年9月21日（周六）上午10:30

报告地点：光电所二层报告厅

**报告摘要：**

Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular – Schrodinger’s equation. If quantum simulators can be useful for simulating Schrodinger’s equation, it is hoped that they may also be helpful for simulating other PDEs. As with large-scale quantum systems, classical methods for other high-dimensional and large-scale PDEs often suffer from the curse-of-dimensionality (costs scale exponentially in the dimension D of the PDE), which a quantum treatment might in certain cases be able to mitigate. To enable simulation of PDEs on quantum devices that obey Schrodinger’s equations, it is crucial to first develop good methods for mapping other PDEs onto Schrodinger’s equations.

In this talk, I will give a reminder of the notion of Schrodingerisation: a procedure for transforming non-Schrodinger PDEs into a Schrodinger-form. This simple methodology can be used directly on analog or continuous quantum degrees of freedom – called qumodes, and not only on qubits. This continuous representation can be more natural for PDEs since, unlike most computational methods, one does not need to discretise the PDE first. In this way, we can directly map D-dimensional linear PDEs onto a (D + 1)-qumode quantum system where analog Hamiltonian simulation on (D + 1) qumodes can be used. I show how this method can also be applied to both autonomous and non-autonomous linear PDEs. In particular, I will provide an update about our methodology for heat-like equations which can be more amenable to nearer-term implementation.

**报告人简介：**

Nana Liu received her doctorate in 2016 from the University of Oxford as a Clarendon Scholar. She was later a Postdoctoral Research Fellow at the Center for Quantum Technologies in the National University of Singapore and the Singapore University of Technology and Design, before joining Shanghai Jiao Tong University in late 2018 and the Institute of Natural Sciences in 2020. Nana is one of MIT Technology Review’s 10 Innovators Under 35 in the Asia-Pacific region for 2019. Her research focus is on employing quantum resources for both quantum computation and sensing. Her research also lies at the interface between quantum computation, security and machine learning, which will be useful in building a future quantum internet.