QLunch: Konstantina Trivisa

Speaker: Konstantina Trivisa, University of Maryland

Title: On efficient quantum algorithms for dissipative nonlinear differential equations and further developments for problems in fluids and biology

Abstract: Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation. This result appeared in Proceedings of the National Academy of Sciences.

I will also present some recent developments on the construction of efficient quantum algorithms for nonlinear models of fractional diffusion equations with potential applications in biology.  This work was recently accepted by the journal Quantum.