mlsanityData to 7 Oct 2026

Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity

arXiv 2406.06482 ↗First posted 10 Jun 2024quant-ph cond-mat.dis-nn cs.ETcited by 9

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Abstract (arXiv)

The widespread adoption of machine learning and artificial intelligence in all branches of science and technology has created a need for energy-efficient, alternative hardware platforms. While such neuromorphic approaches have been proposed and realised for a wide range of platforms, physically extracting the gradients required for training remains challenging as generic approaches only exist in certain cases. Equilibrium propagation (EP) is such a procedure that has been introduced and applied to classical energy-based models which relax to an equilibrium. Here, we show a direct connection between EP and Onsager reciprocity and exploit this to derive a quantum version of EP. This can be used to optimize loss functions that depend on the expectation values of observables of an arbitrary quantum system. Specifically, we illustrate this new concept with supervised and unsupervised learning examples in which the input or the solvable task is of quantum mechanical nature, e.g., the recognition of quantum many-body ground states, quantum phase exploration, sensing and phase boundary exploration. We propose that in the future quantum EP may be used to solve tasks such as quantum phase discovery with a quantum simulator even for Hamiltonians which are numerically hard to simulate or even partially unknown. Our scheme is relevant for a variety of quantum simulation platforms such as ion chains, superconducting qubit arrays, neutral atom Rydberg tweezer arrays and strongly interacting atoms in optical lattices.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 24 of its 61 references that are in the map. First posted on arXiv 10 Jun 2024.

Builds on

24 of 61 references.

References · 24

  1. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 251
  2. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 125
  3. 2020Photonics for artificial intelligence and neuromorphic computingcited by 111
  4. 2018Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architecturescited by 100
  5. 2020Training End-to-End Analog Neural Networks with Equilibrium Propagationcited by 57
  6. 2024Training of Physical Neural Networkscited by 47
  7. 2018Training of photonic neural networks through in situ backpropagationcited by 45
  8. 2022Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networkscited by 43
  9. 2023Backpropagation-free Training of Deep Physical Neural Networkscited by 42
  10. 2023Energy-based learning algorithms for analog computing: a comparative studycited by 36
  11. 2020EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementationscited by 29
  12. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
12 more
  1. 2021Self-learning Machines based on Hamiltonian Echo Backpropagationcited by 28
  2. 2020Equilibrium Propagation with Continual Weight Updatescited by 25
  3. 2021A deep learning theory for neural networks grounded in physicscited by 23
  4. 2023Nonlinear Processing with Linear Opticscited by 19
  5. 2023Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterialcited by 19
  6. 2024Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagationcited by 16
  7. 2022Agnostic Physics-Driven Deep Learningcited by 14
  8. 2023Nonlinear optical encoding enabled by recurrent linear scatteringcited by 14
  9. 2024Equilibrium Propagation: the Quantum and the Thermal Casescited by 9
  10. 2024Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systemscited by 9
  11. 2023Training neural networks with end-to-end optical backpropagationcited by 7
  12. 2023Local minima in quantum systemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 6.

9 papers.

  1. 2025Equilibrium Propagation for Learning in Lagrangian Dynamical Systemscited by 6
  2. 2025Near-Equilibrium Propagation training in nonlinear wave systemscited by 2
  3. 2025Circuit realization and hardware linearization of monotone operator equilibrium networkscited by 1
  4. 2026Training a Predictive Coding Network on ImageNet using Equilibrium Propagationcited by 1
  5. 2026Laser interferometry as a robust neuromorphic platform for machine learningcited by 0
  6. 2026Equilibrium Propagation for Non-Conservative Systemscited by 0
  7. 2026The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networkscited by 0
  8. 2026Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Modelcited by 0
  9. 2026Perturbative Contrastive Physical Learningcited by 0