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arXiv · 2307.07173

Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport

Fong Yew Leong·Dax Enshan Koh·Wei-Bin Ewe·Jian Feng Kong
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Abstract

We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions compared to those with partial or linear entangling layers. To efficiently encode impulse functions, we propose a graphical mapping technique for quantum states that often requires only a single bit-flip of a parametric gate. As a proof of concept, we simulate colloidal deposition on a planar wall by solving the Smoluchowski equation including the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential energy. We find that over-parameterization is necessary to satisfy certain boundary conditions and that higher-order time-stepping can effectively reduce norm errors. Together, our work highlights the potential of variational quantum simulation for solving partial differential equations using near-term quantum devices.

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Fong Yew Leong, Dax Enshan Koh, Wei-Bin Ewe, Jian Feng Kong. 2023-07-14. Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport. https://doi.org/10.1108/hff-05-2023-0265

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