Large-scale Lindblad learning from time-series data

In this work, we develop a protocol for learning a time-independent Lindblad model for operations that can be applied repeatedly on a quantum computer. The protocol is highly scalable for models with local interactions and is in principle insensitive to state-preparation errors. At its core, the protocol forms a linear system of equations for the model parameters in terms of a set of observable values and their gradients. The required gradient information is obtained by fitting time-series data with sums of exponentially damped sinusoids and differentiating those curves. We develop a robust curve-fitting procedure that finds the most parsimonious representation of the data up to shot noise. We demonstrate the approach by learning the Lindbladian for a full layer of gates on a 156-qubit superconducting quantum processor, providing the first learning experiment of this kind. We study the effects of state-preparation and measurement errors and limitations on the operations that can be learned. For improved performance under readout errors, we propose an optional fine-tuning strategy that improves the fit between the time-evolved model and the measured data.