Learning Hamiltonians for solid-state quantum simulators

TL;DR

This paper presents a physics-informed neural network framework that learns effective Hamiltonians directly from experimental data in solid-state quantum systems, enabling automated and accurate characterization of quantum simulators.

Contribution

The authors develop an unsupervised autoencoder-based method embedding physical constraints to learn Hamiltonians from transport measurements, improving interpretability and generalization in solid-state quantum systems.

Findings

Successfully characterized a triple quantum dot chain from transport data

Model generalizes beyond training data to unseen parameter regimes

Robustness to measurement noise demonstrated

Abstract

We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure. Unlike purely data-driven supervised schemes, the proposed unsupervised autoencoder-based method incorporates the governing physics (here, the S-matrix formalism) within the decoder network, ensuring that the learned representations remain physically meaningful. Through numerical learning experiments, we demonstrate automated characterization of programmable solid-state simulators from transport measurements, exemplified by a triple quantum dot chain. The trained model generalizes beyond the training domain and accurately infers Hamiltonian parameters from transport data. While the model has finite capacity -- leading to degraded performance when the parameter space becomes excessively large or structurally diverse -- we identify regimes in which robust generalization is maintained. We further show how to train the model to handle noisy measurements, reflecting realistic experimental conditions.