“Simulating non-linear dynamics on quantum computers: An efficient, scaleable quantum algorithm to integrate non-linear differential equation systems”

ABSTRACT:
Numerous natural science disciplines such as Physics, Engineering and Materials Science rely on efficient methods to integrate non-linear differential equations.  Quantum algorithms are famously known to outperform their classical counterparts on a number of important tasks, such as Fourier Transformations, Singular Value Decompositions, Matrix Inversions and others. Yet all these operations are linear.
For many decades, it was unknown whether a scalable resource-efficient quantum algorithm to integrate non-linear differential equation systems could be developed. In this talk, work will be presented which closes this gap. We will outline a quantum algorithm that utilises mean-field non- linearities. These non-linearities emerge in quantum systems compounded of several identical state copies. Although the evolution of the joint state is governed by the linear Schroedinger equation, the evolution of an individual copy follows – within certain limits – a non-linear differential equation.
Results will be presented on emulating this new algorithm on a classical computer. By integrating a number of toy models, it is possible to get a first glimpse into the potential of the quantum non-linear solver to aid key tasks in various scientific disciplines.
BIOGRAPHY:
Felix Tennie did his undergraduate work in Physics, Mathematics and Music at the Universities of Hamburg, Cambridge and Hanover, respectively. He received his DPhil from the University of Oxford under the supervision of Prof. Vlatko Vedral working on the “Influence of the Exchange Symmetry beyond the Exclusion Principle”. Already during the final year of his doctoral studies, he started working as a Physics lecturer at Lincoln College, University of Oxford. Shortly after the completion of his DPhil, Felix was awarded a Junior Research Fellowship at Wolfson College, University of Oxford. He currently works with Prof. Tim Palmer and Prof. Seth Lloyd on the potential applicability of quantum computing in Weather and Climate Sciences. His research focusses on various aspects of Quantum Information, Quantum Algorithms and Many-Body Physics.