Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems

Abstract

Equilibrium propagation (EP) is a training framework for physical systems that minimize an energy function. EP uses the system's intrinsic physics during both inference and training, making it a candidate for the development of energy-efficient processors for machine learning. EP has been studied in various classical physical systems, including classical Ising networks and elastic networks. We present a version of EP for quantum systems, where the energy function is the Hamiltonian's expectation value, whose minimum is reached at the ground state. As examples, we study the settings of the transverse-field Ising network and the quantum harmonic oscillator network -- quantum analogues of the network models studied within classical EP.