Nonlinear dynamics as a ground-state solution on quantum computers

Nonlinear dynamics as a ground-state solution on quantum computers

Blog Article

For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit Cape 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, 145 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.