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

• URL: http://arxiv.org/abs/2307.07173v1
• Date: Fri, 14 Jul 2023 05:51:57 GMT
• Title: Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport
• Authors: Fong Yew Leong, Dax Enshan Koh, Wei-Bin Ewe and Jian Feng Kong
• Abstract summary: We show that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions. To efficiently encode impulse functions, we propose a graphical mapping technique for quantum states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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