Learning Arbitrary Lindbladians from Time Evolution
Abstract
We study the problem of learning arbitrary n-qubit Lindbladians, the generators of Markovian open-system dynamics, from their time evolution. We give the first known efficient algorithm that learns arbitrary Lindbladians without any structural assumptions. For an n-qubit Lindbladian of dynamical strength at most Λ, the algorithm estimates every coefficient to error ε using Õ(Λ2/ε2) experiments and Õ(Λ/ε2) total evolution time, with classical running time polynomial in n and Λ/ε. Both experimental costs match known lower bounds up to polylogarithmic factors. The algorithm identifies candidate labels through product Pauli experiments and estimates their coefficients using random stabilizer preparations and Clifford measurements. It requires no ancillas or control during the unknown evolution. For constant k, our algorithm learns generic k-local Lindbladians of local dynamical strength at most Λloc using Õ(n2Λloc2/ε2) experiments and Õ(nΛloc/ε2) total evolution time, improving the upper bounds of prior works in terms of the dependence on n. We further improve the lower bounds of Arad, Chen, Guo, Rebentrost, and Yu (SODA 2027) using a family of $3$-local Lindbladians. They already hold when the support is known, and only one Hamiltonian coefficient is requested, even for adaptive protocols with arbitrary ancillas and quantum memory. These lower bounds establish that our algorithm is optimal up to polylogarithmic factors in both experiment count and total evolution time for every fixed k ≥ 3.
Related
- Learning Arbitrary Lindbladians with Quantum Error Correction
- Robust Structure Learning of k-local Lindbladians
- Learning Local Fermionic Lindbladians under Parity Superselection
- Near-Optimal Learning of Local Lindbladians
- Bosonization for the Schwinger effect at small fermion mass: analytic formula for the 1+1D current in an arbitrary time-dependent, inhomogeneous electric field
BibTeX
@misc{chen2026learning,
title = {{Learning Arbitrary Lindbladians from Time Evolution}},
author = {Zhili Chen and Zhan Yu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.28610},
eprint = {2607.28610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28610},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning Arbitrary Lindbladians from Time Evolution
AU - Zhili Chen
AU - Zhan Yu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.28610
UR - https://arxiv.org/abs/2607.28610
AB - We study the problem of learning arbitrary n-qubit Lindbladians, the generators of Markovian open-system dynamics, from their time evolution. We give the first known efficient algorithm that learns arbitrary Lindbladians without any structural assumptions. For an n-qubit Lindbladian of dynamical strength at most Λ, the algorithm estimates every coefficient to error ε using Õ(Λ^2/ε^2) experiments and Õ(Λ/ε^2) total evolution time, with classical running time polynomial in n and Λ/ε. Both experimental costs match known lower bounds up to polylogarithmic factors. The algorithm identifies candidate labels through product Pauli experiments and estimates their coefficients using random stabilizer preparations and Clifford measurements. It requires no ancillas or control during the unknown evolution. For constant k, our algorithm learns generic k-local Lindbladians of local dynamical strength at most Λ_loc using Õ(n^2Λ_loc^2/ε^2) experiments and Õ(nΛ_loc/ε^2) total evolution time, improving the upper bounds of prior works in terms of the dependence on n. We further improve the lower bounds of Arad, Chen, Guo, Rebentrost, and Yu (SODA 2027) using a family of $3$-local Lindbladians. They already hold when the support is known, and only one Hamiltonian coefficient is requested, even for adaptive protocols with arbitrary ancillas and quantum memory. These lower bounds establish that our algorithm is optimal up to polylogarithmic factors in both experiment count and total evolution time for every fixed k ≥ 3.
ER -