Equilibrium propagation in non-equilibrium quantum systems
Abstract
Equilibrium propagation (EP) is a powerful training algorithm for self-learning physical systems that is widely used for a variety of machine learning inspired tasks. It relies on the existence of an energy function that depends on tunable training parameters, and can be extended to apply to many-body quantum systems in equilibrium. A key challenge however is the need to repeatedly relax to the system ground state after each parameter update. We show here a route for circumventing this problem by extending EP to many-body driven-dissipative quantum systems, where the dynamics naturally relaxes to a parameter-dependent non-equilibrium steady state. Despite the lack of a free energy, we find that for a class of open systems, a quantum detailed balance symmetry still allows for an efficient EP strategy. This relies crucially on a new class of non-equilibrium static susceptibility relations that we derive in detail. We analyze examples of our new non-equilibrium training paradigm for two experimentally-relevant models: a driven-dissipative transverse field Ising model, and a parametrically-driven bosonic lattice.
Related
- Quantum electrodynamics of equilibrium systems: A rigorous Maxwell-regularized functional-theoretic formulation
- Restricted typicality in non-equilibrium quantum many-body systems
- Temperature Beyond Equilibrium in Isolated Quantum Many-Body Systems and Their Subsystems
- Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems
- On the relaxation dynamics of non-equilibrium quantum systems
BibTeX
@misc{gandotra2026equilibrium,
title = {{Equilibrium propagation in non-equilibrium quantum systems}},
author = {Aditya Gandotra and David D. Noachtar and Aashish A. Clerk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35585},
eprint = {2610.35585},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35585},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Equilibrium propagation in non-equilibrium quantum systems
AU - Aditya Gandotra
AU - David D. Noachtar
AU - Aashish A. Clerk
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35585
UR - https://arxiv.org/abs/2610.35585
AB - Equilibrium propagation (EP) is a powerful training algorithm for self-learning physical systems that is widely used for a variety of machine learning inspired tasks. It relies on the existence of an energy function that depends on tunable training parameters, and can be extended to apply to many-body quantum systems in equilibrium. A key challenge however is the need to repeatedly relax to the system ground state after each parameter update. We show here a route for circumventing this problem by extending EP to many-body driven-dissipative quantum systems, where the dynamics naturally relaxes to a parameter-dependent non-equilibrium steady state. Despite the lack of a free energy, we find that for a class of open systems, a quantum detailed balance symmetry still allows for an efficient EP strategy. This relies crucially on a new class of non-equilibrium static susceptibility relations that we derive in detail. We analyze examples of our new non-equilibrium training paradigm for two experimentally-relevant models: a driven-dissipative transverse field Ising model, and a parametrically-driven bosonic lattice.
ER -