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Main Authors: Leong, Fong Yew, Koh, Dax Enshan, Ewe, Wei-Bin, Kong, Jian Feng
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2307.07173
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author Leong, Fong Yew
Koh, Dax Enshan
Ewe, Wei-Bin
Kong, Jian Feng
author_facet Leong, Fong Yew
Koh, Dax Enshan
Ewe, Wei-Bin
Kong, Jian Feng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_07173
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport
Leong, Fong Yew
Koh, Dax Enshan
Ewe, Wei-Bin
Kong, Jian Feng
Quantum Physics
Computational Physics
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.
title Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport
topic Quantum Physics
Computational Physics
url https://arxiv.org/abs/2307.07173