Thermodynamic Matrix Exponentials and Thermodynamic Parallelism
- URL: http://arxiv.org/abs/2311.12759v2
- Date: Fri, 5 Jan 2024 13:00:48 GMT
- Title: Thermodynamic Matrix Exponentials and Thermodynamic Parallelism
- Authors: Samuel Duffield, Maxwell Aifer, Gavin Crooks, Thomas Ahle, and Patrick
J. Coles
- Abstract summary: We show that certain linear algebra problems can be solved thermodynamically, leading to an speedup scaling with the matrix dimension.
The origin of this "thermodynamic advantage" has not yet been fully explained, and it is not clear what other problems might benefit from it.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Thermodynamic computing exploits fluctuations and dissipation in physical
systems to efficiently solve various mathematical problems. For example, it was
recently shown that certain linear algebra problems can be solved
thermodynamically, leading to an asymptotic speedup scaling with the matrix
dimension. The origin of this "thermodynamic advantage" has not yet been fully
explained, and it is not clear what other problems might benefit from it. Here
we provide a new thermodynamic algorithm for exponentiating a real matrix, with
applications in simulating linear dynamical systems. We describe a simple
electrical circuit involving coupled oscillators, whose thermal equilibration
can implement our algorithm. We also show that this algorithm also 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, and we hypothesize this as a mechanism to explain thermodynamic
advantage more generally.
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