Analog quantum simulation of partial differential equations

报告题目:Analog quantum simulation of partial differential equations

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

报告时间:2023年9月15日(周五) 下午 5:00



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 introduce 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 be applied to linear PDEs, certain nonlinear PDEs, nonlinear ODEs and also linear PDEs with random coefficients, which is important in uncertainty quantification.


Nana Liu is a professor and PI of the Quantum Information and Technologies (QIT) group in the Institute of Natural Sciences at Shanghai Jiao Tong University and the University of Michigan-Shanghai Jiao Tong University Joint Institute. She obtained her BS and MS from the University of Melbourne, majoring in pure mathematics and physics. She received her PhD from the University of Oxford as a Clarendon Scholar, specializing in quantum protocols for computation and sensing. She then became a Postdoctoral Research Fellow at the Center for Quantum Technologies in the National University of Singapore and the Singapore University of Technology and Design. She is the 2019 recipient of the MIT Technology Review’s 10 Innovators under 35 in the Asia-Pacific region for her work on quantum protocols at the interface between quantum computation and security. Her current research interests include quantum algorithms for scientific computing and quantum protocols relevant for a future quantum internet. She is also an editorial board member of the journals Quantum Science and Technology, Intelligent Machine (Science partner journal) and has been program committee chair for Quantum Techniques in Machine Learning and QTurn.