Thermodynamic matrix exponentials and thermodynamic parallelism
Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. It was recently shown that certain linear algebra problems can be solved thermodynamically, leading to a speedup scaling with the matrix dimension. Here, we provide a...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-02-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013147 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823859956693073920 |
|---|---|
| author | Samuel Duffield Maxwell Aifer Gavin Crooks Thomas Ahle Patrick J. Coles |
| author_facet | Samuel Duffield Maxwell Aifer Gavin Crooks Thomas Ahle Patrick J. Coles |
| author_sort | Samuel Duffield |
| collection | DOAJ |
| description | Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. It was recently shown that certain linear algebra problems can be solved thermodynamically, leading to a speedup scaling with the matrix dimension. Here, we provide a thermodynamic algorithm for exponentiating a real matrix. We describe a simple electrical circuit involving coupled oscillators, which can implement our algorithm. We also show that this algorithm provides an asymptotic speedup that is linear in the dimension. Finally, we introduce the concept of thermodynamic parallelism to explain this speedup, stating that thermodynamic noise provides a resource leading to effective parallelization of computations. |
| format | Article |
| id | doaj-art-124da3b74b2a461081aebf5b32be7047 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-124da3b74b2a461081aebf5b32be70472025-02-10T17:16:41ZengAmerican Physical SocietyPhysical Review Research2643-15642025-02-017101314710.1103/PhysRevResearch.7.013147Thermodynamic matrix exponentials and thermodynamic parallelismSamuel DuffieldMaxwell AiferGavin CrooksThomas AhlePatrick J. ColesThermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. It was recently shown that certain linear algebra problems can be solved thermodynamically, leading to a speedup scaling with the matrix dimension. Here, we provide a thermodynamic algorithm for exponentiating a real matrix. We describe a simple electrical circuit involving coupled oscillators, which can implement our algorithm. We also show that this algorithm provides an asymptotic speedup that is linear in the dimension. Finally, we introduce the concept of thermodynamic parallelism to explain this speedup, stating that thermodynamic noise provides a resource leading to effective parallelization of computations.http://doi.org/10.1103/PhysRevResearch.7.013147 |
| spellingShingle | Samuel Duffield Maxwell Aifer Gavin Crooks Thomas Ahle Patrick J. Coles Thermodynamic matrix exponentials and thermodynamic parallelism Physical Review Research |
| title | Thermodynamic matrix exponentials and thermodynamic parallelism |
| title_full | Thermodynamic matrix exponentials and thermodynamic parallelism |
| title_fullStr | Thermodynamic matrix exponentials and thermodynamic parallelism |
| title_full_unstemmed | Thermodynamic matrix exponentials and thermodynamic parallelism |
| title_short | Thermodynamic matrix exponentials and thermodynamic parallelism |
| title_sort | thermodynamic matrix exponentials and thermodynamic parallelism |
| url | http://doi.org/10.1103/PhysRevResearch.7.013147 |
| work_keys_str_mv | AT samuelduffield thermodynamicmatrixexponentialsandthermodynamicparallelism AT maxwellaifer thermodynamicmatrixexponentialsandthermodynamicparallelism AT gavincrooks thermodynamicmatrixexponentialsandthermodynamicparallelism AT thomasahle thermodynamicmatrixexponentialsandthermodynamicparallelism AT patrickjcoles thermodynamicmatrixexponentialsandthermodynamicparallelism |