Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions
In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013038 |
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| _version_ | 1841546913010155520 |
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| author | Tong Jiang Bryan O'Gorman Ankit Mahajan Joonho Lee |
| author_facet | Tong Jiang Bryan O'Gorman Ankit Mahajan Joonho Lee |
| author_sort | Tong Jiang |
| collection | DOAJ |
| description | In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a crucial subroutine in MPS-AFQMC, is proven to be #P-hard. Nonetheless, we tested several promising heuristics in successfully improving fermionic phaseless AFQMC energies. We also proposed a way to evaluate local energy and force bias evaluations free of matrix product operators. This allows for larger basis set calculations without significant overhead. We showcase the utility of our approach on one- and two-dimensional hydrogen lattices, even when the MPS trial itself struggles to obtain high accuracy. Our work offers a new set of tools that can solve currently challenging electronic structure problems with future improvements. |
| format | Article |
| id | doaj-art-dff1056e96bc41af9ccde5d925cd8588 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-dff1056e96bc41af9ccde5d925cd85882025-01-10T15:04:51ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101303810.1103/PhysRevResearch.7.013038Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctionsTong JiangBryan O'GormanAnkit MahajanJoonho LeeIn this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a crucial subroutine in MPS-AFQMC, is proven to be #P-hard. Nonetheless, we tested several promising heuristics in successfully improving fermionic phaseless AFQMC energies. We also proposed a way to evaluate local energy and force bias evaluations free of matrix product operators. This allows for larger basis set calculations without significant overhead. We showcase the utility of our approach on one- and two-dimensional hydrogen lattices, even when the MPS trial itself struggles to obtain high accuracy. Our work offers a new set of tools that can solve currently challenging electronic structure problems with future improvements.http://doi.org/10.1103/PhysRevResearch.7.013038 |
| spellingShingle | Tong Jiang Bryan O'Gorman Ankit Mahajan Joonho Lee Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions Physical Review Research |
| title | Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions |
| title_full | Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions |
| title_fullStr | Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions |
| title_full_unstemmed | Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions |
| title_short | Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions |
| title_sort | unbiasing fermionic auxiliary field quantum monte carlo with matrix product state trial wavefunctions |
| url | http://doi.org/10.1103/PhysRevResearch.7.013038 |
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