Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems
This work addresses the challenge of training quantum systems for machine learning, offering a potential method for energy-efficient quantum processors, though it appears incremental as it adapts an existing classical framework to quantum settings.
The authors extended the Equilibrium Propagation training framework to quantum systems, enabling gradient-descent training by minimizing the mean energy functional, and demonstrated this on quantum analogues like the transverse-field Ising model and quantum harmonic oscillator network.
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.