Experimental quantum Hamiltonian learning

The efficient characterization and validation of the underlying model of a quantum physical system is a central challenge in the development of quantum techonologies. Quantum Hamiltonian Learning (QHL) combines the capabilities of quantum information processing and classical machine learning to allow the efficient characterization of the model of quantum systems. The behavior of a quantum Hamiltonian model can be efficiently predicted by a quantum simulator, and the predictions are contrasted with the data obtained from the system to infer its Hamiltonian via Bayesian methods.

Our experimental demonstration of QHL uses a programmable silicon-photonics quantum simulator to learn the electron spin dynamics of a nitrogen-vacancy centre in diamond. The spin is optically addressed and read-out and manipluated by microwave signals. The dynamics can be described using a Hamiltonian model fσ_x/2. The photonic chip allows to simulate the dynamics of the spin and to calculate the QHL likelihoods. The two quantum systems are interfaced through a classical processor drives the QHL protocol. The goal is to learn the Rabi frequency f of the spin system. We show the successful convergence of the QHL, with a learned f=6.93±0.09 MHz consistent with that obtained from the standard methods.