Learning the structure of open quantum systems

2026-06-29

AI Summary

This work addresses the challenge of learning both the structure and parameters of Lindbladians governing open quantum systems. It proposes an efficient iterative algorithm that recovers the coefficients of an $n$-qubit, constant-locality Lindbladian from time-evolution data using only non-adaptive, ancilla-free random Pauli measurements, without requiring prior knowledge of the underlying interaction graph. The method achieves, for the first time, efficient structure learning for Lindbladians with quasi-local or power-law interactions and extends naturally to Hamiltonian structure learning from high-temperature Gibbs states. Based on Fourier coefficient optimization, the algorithm excels under limited interference conditions, attaining $\varepsilon$ accuracy with total evolution time $O(g d^2 \log n / \varepsilon^2)$ and temporal resolution $\Theta(1/g)$.

Abstract

We design an algorithm for learning the coefficients of an $n$-qubit constant-local Lindbladian to $\varepsilon$ error with $O(g d^2 \log(n) / \varepsilon^2)$ 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. 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.

Problem

• open quantum systems
• Lindbladian learning
• structure learning
• quantum dynamics
• Hamiltonian learning

Innovation

• Lindbladian learning
• open quantum systems
• structure learning
• randomized Pauli measurements
• iterative algorithm