Learning the structure of open quantum systems
Abstract
We design an algorithm for learning the coefficients of an n-qubit constant-local Lindbladian to ε error with O(g d2 log(n) / ε2) total evolution time, where g is the single-site energy and d is the (approximate) degree of the interaction graph. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only Θ(1/g); (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians. Moreover, we prove a lower bound showing that our algorithm is optimal in each parameter up to logarithmic factors. Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, which we call "confusing" terms. For settings where the "confusion" is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.
Related
- Full-Trajectory Learning of Open Quantum Systems: Dynamical Emulation and the Limits of Hamiltonian Identifiability
- Large fluctuations in open quantum systems
- Nambu Nonequilibrium Thermodynamics and the Lyapunov Structure of Open Systems
- Open Quantum Systems
- Dynamical Tensor Train Approximation for Wigner--Fokker--Planck Equation with Applications to Open Quantum Systems
BibTeX
@misc{lewis2026learning,
title = {{Learning the structure of open quantum systems}},
author = {Laura Lewis and Ewin Tang and John Wright},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30358},
eprint = {2606.30358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30358},
}
RIS
TY - UNPB
TI - Learning the structure of open quantum systems
AU - Laura Lewis
AU - Ewin Tang
AU - John Wright
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.30358
UR - https://arxiv.org/abs/2606.30358
AB - We design an algorithm for learning the coefficients of an n-qubit constant-local Lindbladian to ε error with O(g d^2 log(n) / ε^2) total evolution time, where g is the single-site energy and d is the (approximate) degree of the interaction graph. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only Θ(1/g); (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians. Moreover, we prove a lower bound showing that our algorithm is optimal in each parameter up to logarithmic factors. Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, which we call "confusing" terms. For settings where the "confusion" is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.
ER -