Efficient quantum computation of molecular forces and other energy gradients
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecula...
| Main Authors: | , , , , , , , , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043210 |
| _version_ | 1797210576201449472 |
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| author | Thomas E. O'Brien Michael Streif Nicholas C. Rubin Raffaele Santagati Yuan Su William J. Huggins Joshua J. Goings Nikolaj Moll Elica Kyoseva Matthias Degroote Christofer S. Tautermann Joonho Lee Dominic W. Berry Nathan Wiebe Ryan Babbush |
| author_facet | Thomas E. O'Brien Michael Streif Nicholas C. Rubin Raffaele Santagati Yuan Su William J. Huggins Joshua J. Goings Nikolaj Moll Elica Kyoseva Matthias Degroote Christofer S. Tautermann Joonho Lee Dominic W. Berry Nathan Wiebe Ryan Babbush |
| author_sort | Thomas E. O'Brien |
| collection | DOAJ |
| description | While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications such as molecular dynamics simulations. Here, we introduce new quantum algorithms for computing molecular energy derivatives with significantly lower complexity than prior methods. Under cost models appropriate for noisy-intermediate scale quantum devices, we demonstrate how low-rank factorization and other tomography schemes can be optimized for energy derivative calculations. We numerically demonstrate that our techniques reduce the number of circuit repetitions required by many orders of magnitude for even modest systems, and that the cost of estimating an entire force vector may in some systems be lower than the cost of estimating the energy. In the context of fault-tolerant algorithms, we develop new methods of estimating energy derivatives with Heisenberg limited scaling, incorporating state-of-the-art techniques for block encoding fermionic operators. In contrast to our near-term results, we find that the cost of estimating forces with any of our Heisenberg-limited methods is bounded by the cost of estimating energies, due to inner loops requiring either energy estimation or reflections around the ground state. This implies that applications such as geometry optimization, coupling parameter estimation, and spectral prediction may be practical on fault-tolerant quantum devices, but tractable molecular dynamics simulations of large-scale systems requires further algorithmic advances. |
| first_indexed | 2024-04-24T10:12:47Z |
| format | Article |
| id | doaj.art-5cede1d0c45840d6b4389cabde88e8f9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:47Z |
| publishDate | 2022-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-5cede1d0c45840d6b4389cabde88e8f92024-04-12T17:27:17ZengAmerican Physical SocietyPhysical Review Research2643-15642022-12-014404321010.1103/PhysRevResearch.4.043210Efficient quantum computation of molecular forces and other energy gradientsThomas E. O'BrienMichael StreifNicholas C. RubinRaffaele SantagatiYuan SuWilliam J. HugginsJoshua J. GoingsNikolaj MollElica KyosevaMatthias DegrooteChristofer S. TautermannJoonho LeeDominic W. BerryNathan WiebeRyan BabbushWhile most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications such as molecular dynamics simulations. Here, we introduce new quantum algorithms for computing molecular energy derivatives with significantly lower complexity than prior methods. Under cost models appropriate for noisy-intermediate scale quantum devices, we demonstrate how low-rank factorization and other tomography schemes can be optimized for energy derivative calculations. We numerically demonstrate that our techniques reduce the number of circuit repetitions required by many orders of magnitude for even modest systems, and that the cost of estimating an entire force vector may in some systems be lower than the cost of estimating the energy. In the context of fault-tolerant algorithms, we develop new methods of estimating energy derivatives with Heisenberg limited scaling, incorporating state-of-the-art techniques for block encoding fermionic operators. In contrast to our near-term results, we find that the cost of estimating forces with any of our Heisenberg-limited methods is bounded by the cost of estimating energies, due to inner loops requiring either energy estimation or reflections around the ground state. This implies that applications such as geometry optimization, coupling parameter estimation, and spectral prediction may be practical on fault-tolerant quantum devices, but tractable molecular dynamics simulations of large-scale systems requires further algorithmic advances.http://doi.org/10.1103/PhysRevResearch.4.043210 |
| spellingShingle | Thomas E. O'Brien Michael Streif Nicholas C. Rubin Raffaele Santagati Yuan Su William J. Huggins Joshua J. Goings Nikolaj Moll Elica Kyoseva Matthias Degroote Christofer S. Tautermann Joonho Lee Dominic W. Berry Nathan Wiebe Ryan Babbush Efficient quantum computation of molecular forces and other energy gradients Physical Review Research |
| title | Efficient quantum computation of molecular forces and other energy gradients |
| title_full | Efficient quantum computation of molecular forces and other energy gradients |
| title_fullStr | Efficient quantum computation of molecular forces and other energy gradients |
| title_full_unstemmed | Efficient quantum computation of molecular forces and other energy gradients |
| title_short | Efficient quantum computation of molecular forces and other energy gradients |
| title_sort | efficient quantum computation of molecular forces and other energy gradients |
| url | http://doi.org/10.1103/PhysRevResearch.4.043210 |
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