The Governing Council of the University of Toronto

Purpose

The aim of the project is to develop new approaches to differential equations with an aim of providing clear exponential advantages for problems in plasma physics, geo physics, optimization, financial mathematics and chemistry. The project will extend current approaches to handle stochastic differential equations and build quantum algorithms for inverse problems where a partial solution is known at different times in the dynamics. These will open up applications in geophysics and financial mathematics that at present are impossible on quantum computers. The team will develop a new mathematical formalism that proves bounds on information propagation speed to simplify both quantum and classical differential equation algorithms, also leading to new methods of simulating relativistic dynamics on quantum computers. Finally, the project will examine applications of these ideas to the aforementioned domain sciences and aim to show clear evidence for an end-to-end quantum advantage that could revolutionize the Canadian economy and scientific community.