Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.07173 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913425877106688 |
|---|---|
| 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 |