Hamiltonian Learning at Scale
Abstract
Learning a quantum system's Hamiltonian is crucial for understanding and controlling its dynamics and has recently become a topic of widespread interest. To understand the learning protocol's error tolerances, i.e. its stability in the presence of inevitable errors, this work utilizes tensor network techniques to emulate Hamiltonian learning workflows at scale and with noise. Specifically, we employed a Hamiltonian learning technique based on approximate stationary states which are constructed using matrix product tools. We provide analytic bounds on the Hamiltonian learning estimation errors and perform numerical simulations that highlight learning error's stability under two families of errors. Using our workflow, we are able to scale up the protocol and learn mixed-field Ising model Hamiltonians of an N=300 site spin chain. By simulating the protocol at large scale, and empirically studying its practical limitations, our analysis of how errors affect the Hamiltonian learning process provides valuable lessons for future experiments. We conclude by discussing the avenues our work opens as well as future work that can support Hamiltonian learning experiments.
Related
- Comment on "Supervised Learning with Quantum Hamiltonian Embeddings" (arXiv:2610.26833)
- Quantum Sensing and Hamiltonian Learning under Stochastic Parameter Evolution
- Efficient Hamiltonian, structure and trace distance learning of Gaussian states.
- Quantum Hamiltonian Evolution for Coherent Quantum Learning
- Hamiltonian learning reveals optoelectronic mechanisms across thermodynamic state space in soft semiconductors
BibTeX
@misc{johnson2026hamiltonian,
title = {{Hamiltonian Learning at Scale}},
author = {Nathan Johnson and Eugene Dumitrescu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23707},
eprint = {2608.23707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23707},
}
RIS
TY - UNPB
TI - Hamiltonian Learning at Scale
AU - Nathan Johnson
AU - Eugene Dumitrescu
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.23707
UR - https://arxiv.org/abs/2608.23707
AB - Learning a quantum system's Hamiltonian is crucial for understanding and controlling its dynamics and has recently become a topic of widespread interest. To understand the learning protocol's error tolerances, i.e. its stability in the presence of inevitable errors, this work utilizes tensor network techniques to emulate Hamiltonian learning workflows at scale and with noise. Specifically, we employed a Hamiltonian learning technique based on approximate stationary states which are constructed using matrix product tools. We provide analytic bounds on the Hamiltonian learning estimation errors and perform numerical simulations that highlight learning error's stability under two families of errors. Using our workflow, we are able to scale up the protocol and learn mixed-field Ising model Hamiltonians of an N=300 site spin chain. By simulating the protocol at large scale, and empirically studying its practical limitations, our analysis of how errors affect the Hamiltonian learning process provides valuable lessons for future experiments. We conclude by discussing the avenues our work opens as well as future work that can support Hamiltonian learning experiments.
ER -