Hamiltonian Learning via Inverse Physics-Informed Neural Networks

TL;DR

This paper introduces iPINN-HL, a physics-informed neural network approach for Hamiltonian learning that improves accuracy, noise robustness, and resource efficiency by integrating physical laws into the learning process.

Contribution

The paper presents a novel inverse physics-informed neural network method for Hamiltonian learning that outperforms existing deep learning approaches in quantum system characterization.

Findings

Approaches the Heisenberg limit in accuracy.

Demonstrates robustness to noise.

Outperforms DNN-HL in resource efficiency.

Abstract

Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource efficiency, especially under limited measurements. In this work, we present \textit{Inverse Physics-Informed Neural Networks for Hamiltonian Learning (iPINN-HL)}, an approach that incorporates the Schr\"{o}dinger equation as a soft constraint via a loss function penalty into the ML procedure. This formulation allows the model to integrate both observational data and known physical laws to infer Hamiltonian parameters with greater accuracy and resource efficiency. We benchmark iPINN-HL against a deep-neural-network-based quantum state tomography method (denoted as DNN-HL) and demonstrate its effectiveness across several different scenarios, including one-dimensional spin chains, cross-resonance gate calibration, crosstalk identification, and real-time compensation to parameter drift. Our results show that iPINN-HL can approach the Heisenberg limit and exhibits robustness to noises, while outperforming DNN-HL in accuracy and resource efficiency. Therefore, iPINN-HL is a powerful and flexible framework for quantum system characterization for practical tasks.