Nonlinear dynamics as a ground-state solution on quantum computers
For the solution of time-dependent nonlinear differential equations, we
present variational quantum algorithms (VQAs) that encode both space and time
in qubit registers. The spacetime encoding enables us to obtain the entire time
evolution from a single ground-state computation. We describe a general
procedure to construct efficient quantum circuits for the cost function
evaluation required by VQAs. To mitigate the barren plateau problem during the
optimization, we propose an adaptive multigrid strategy. The approach is
illustrated for the nonlinear Burgers equation. We classically optimize quantum
circuits to represent the desired ground-state solutions, run them on IBM Q
System One and Quantinuum System Model H1, and demonstrate that current quantum
computers are capable of accurately reproducing the exact results.
Albert J. Pool Alejandro D. Somoza Conor Mc Keever Michael Lubasch Birger Horstmann