Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems

TL;DR

This paper extends equilibrium propagation to quantum systems, enabling gradient descent training of quantum energy-based models by leveraging the system's physics to compute weight gradients.

Contribution

It introduces a novel framework for quantum equilibrium propagation, applying it to quantum models like the transverse-field Ising model and quantum harmonic oscillators.

Findings

Demonstrates gradient descent training in quantum systems

Extends classical energy-based learning to quantum domain

Provides examples with quantum Ising model and harmonic oscillators

Abstract

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.