mlsanityData to 7 Oct 2026

Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems

arXiv 2406.00879 ↗First posted 2 Jun 2024quant-ph cond-mat.dis-nn cs.LGcited by 9

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Abstract (arXiv)

Equilibrium propagation (EP) is a training framework for energy-based systems, i.e. systems whose physics minimizes an energy function. EP has been explored in various classical physical systems such as resistor networks, elastic networks, the classical Ising model and coupled phase oscillators. A key advantage of EP is that it achieves gradient descent on a cost function using the physics of the system to extract the weight gradients, making it a candidate for the development of energy-efficient processors for machine learning. We extend EP to quantum systems, where the energy function that is minimized is the mean energy functional (expectation value of the Hamiltonian), whose minimum is the ground state of the Hamiltonian. As examples, we study the settings of the transverse-field Ising model and the quantum harmonic oscillator network -- quantum analogues of the Ising model and elastic network.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 18 of its 29 references that are in the map. First posted on arXiv 2 Jun 2024.

Builds on

18 of 29 references.

References · 18

  1. 2020Variational Quantum Algorithmscited by 687
  2. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 251
  3. 2020Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Biascited by 60
  4. 2020Training End-to-End Analog Neural Networks with Equilibrium Propagationcited by 57
  5. 2022Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillationscited by 40
  6. 2023Energy-based learning algorithms for analog computing: a comparative studycited by 36
  7. 2020EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementationscited by 29
  8. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
  9. 2021Self-learning Machines based on Hamiltonian Echo Backpropagationcited by 28
  10. 2022Beyond backpropagation: bilevel optimization through implicit differentiation and equilibrium propagationcited by 26
  11. 2021A deep learning theory for neural networks grounded in physicscited by 23
  12. 2023Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterialcited by 19
6 more
  1. 2024Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagationcited by 16
  2. 2021A contrastive rule for meta-learningcited by 14
  3. 2022Agnostic Physics-Driven Deep Learningcited by 14
  4. 2024Equilibrium Propagation: the Quantum and the Thermal Casescited by 9
  5. 2023Flexible Phase Dynamics for Bio-Plausible Contrastive Learningcited by 4
  6. 2024Training all-mechanical neural networks for task learning through in situ backpropagationcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 5.

9 papers.

  1. 2024Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocitycited by 9
  2. 2025Towards the Training of Deeper Predictive Coding Neural Networkscited by 7
  3. 2025Equilibrium Propagation for Learning in Lagrangian Dynamical Systemscited by 6
  4. 2025Near-Equilibrium Propagation training in nonlinear wave systemscited by 2
  5. 2026Training a Predictive Coding Network on ImageNet using Equilibrium Propagationcited by 1
  6. 2026Laser interferometry as a robust neuromorphic platform for machine learningcited by 0
  7. 2026Equilibrium Propagation for Non-Conservative Systemscited by 0
  8. 2026Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Modelcited by 0
  9. 2026Perturbative Contrastive Physical Learningcited by 0