Quantum equilibrium propagation: Gradient-descent training of quantum systems

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. Here, we derive a version of EP for quantum systems in which the Hamiltonian’s expectation value serves as the energy function, with the minimum corresponding to the ground state. As illustrations, we consider the transverse-field Ising network and the quantum harmonic oscillator network, which are quantum analogs of the network models studied within classical EP.