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QI: Fachverband Quanteninformation

QI 27: Quantum Simulation II

QI 27.10: Talk

Thursday, March 21, 2024, 17:30–17:45, HFT-FT 101

Nonlinear dynamics as a ground-state solution on quantum computers — •Albert Pool^1,2, Alejandro Somoza^1,2, Michael Lubasch³, Conor Mc Keever³, and Birger Horstmann^1,2,4 — ¹Institute of Engineering Thermodynamics, German Aerospace Center (DLR), Ulm, Germany — ²Helmholtz Institute Ulm, Ulm, Germany — ³Quantinuum, London, UK — ⁴Department of Physics, Ulm University, Ulm, Germany

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 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 demonstrate that current quantum computers are capable of accurately reproducing the exact results.