Quantum 2025 – scientific programme
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MON: Monday Contributed Sessions
MON 18: Quantum Algorithms
MON 18.3: Talk
Monday, September 8, 2025, 17:00–17:15, ZHG007
Influence of different feature maps on solving partial differential equations on quantum computers — •David Steffen1,2, Michael Schelling1,2, Felix Schwab1,2, and Birger Horstmann1,2,3 — 1Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Wilhelm-Runge-Str. 10, 89081 Ulm — 2Helmholtz Institute Ulm, Helmholtzstr. 11, 89081 Ulm — 3Department of Physics, Ulm University, Albert-Einstein-Allee 11, 89081 Ulm
Differentiable quantum circuits (DQCs) [1] are variational algorithms to solve partial differential equations on quantum computers. We investigate the potential of this method to solve systems of coupled partial differential equations as they occur in the simulation of electrochemical systems, e.g., fuel cells and batteries. A crucial part of DQCs is the feature space in which the input variables are encoded into quantum states. Possible choices are a Chebyshev feature map or a Fourier feature map, that generate a set of corresponding basis functions to fit the desired model. We show results on the influence of different feature maps on the expressibility and trainability for spatiotemporal models, on the use case of transport equations from battery simulation.
[1] Kyriienko, O. et al., Phys. Rev. A 2021, 103, 052416
Keywords: quantum computing; battery simulation; partial differential equations; variational quantum algorithm