Learning Arbitrary Lindbladians from Time Evolution

Learning the dynamics of open quantum systems is a fundamental challenge in quantum science, as real-world devices are rarely closed and suffer from dissipation, dephasing, and noise. While previous methods for learning Lindbladians often relied on structural promises like locality or sparsity, these assumptions can be restrictive or unrealistic for complex systems. This paper addresses the question: Can an arbitrary Lindbladian be efficiently learned from its time evolution without prior structural assumptions?

The authors propose a two-stage, ancilla-free, and control-free algorithm that requires only a known upper bound on the system's dynamical strength. The first stage, support learning, identifies a polynomial-sized candidate support containing all coefficients above a specific threshold using product Pauli eigenstates and single-qubit measurements. The second stage, coefficient learning, uses randomized Clifford probes to estimate the coefficients within that candidate support. By composing these stages, the algorithm achieves entrywise accuracy for any Lindbladian in polynomial time.

The study demonstrates that the global dynamical strength of a Lindbladian is sufficient to control the complexity of learning its coefficients. The proposed algorithm achieves an experiment count of $\widetilde{O}(\Lambda^2/\epsilon^2)$ and a total evolution time of $\widetilde{O}(\Lambda/\epsilon^2)$, where $\Lambda$ is the dynamical strength and $\epsilon$ is the target error. These results match established information-theoretic lower bounds up to logarithmic factors, making the algorithm nearly optimal. Unlike prior approaches, this method does not require ancillas, coherent control, or a coefficient gap, and it remains efficient even for dense, non-local generators.

This work provides a robust, general-purpose tool for characterizing quantum noise and dissipation in arbitrary systems. By removing the need for structural assumptions like locality or sparsity, the algorithm is applicable to a wider range of quantum devices, including those with complex crosstalk or long-range dissipative processes. The efficiency and simplicity of the protocol—requiring only standard Pauli-basis measurements—make it highly practical for the calibration and certification of near-term quantum hardware.