Near-Optimal Learning of Local Lindbladians
Abstract
We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most Λ, we design an algorithm that learns the coefficients to target accuracy ε, whose experiment count and total evolution time scale as Õ(Λ2/ε2) and Õ(Λ/ε2), respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires Ω(Λ2/ε2) experiments and Ω(Λ/ε2) total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.
Related
- Robust Structure Learning of k-local Lindbladians
- Learning Local Fermionic Lindbladians under Parity Superselection
- Optimal relaxation for Witten Lindbladians
- Near-Optimal Bounds on the Density of Low-Energy States of k-Local Hamiltonians and Faster Quantum Algorithms
- Eigenoperator Entanglement Statistics in Local Lindbladians
BibTeX
@misc{arad2026nearoptimal,
title = {{Near-Optimal Learning of Local Lindbladians}},
author = {Itai Arad and Zhili Chen and Naixu Guo and Patrick Rebentrost and Zhan Yu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.20535},
eprint = {2606.20535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20535},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Near-Optimal Learning of Local Lindbladians
AU - Itai Arad
AU - Zhili Chen
AU - Naixu Guo
AU - Patrick Rebentrost
AU - Zhan Yu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.20535
UR - https://arxiv.org/abs/2606.20535
AB - We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most Λ, we design an algorithm that learns the coefficients to target accuracy ε, whose experiment count and total evolution time scale as Õ(Λ^2/ε^2) and Õ(Λ/ε^2), respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires Ω(Λ^2/ε^2) experiments and Ω(Λ/ε^2) total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.
ER -