Compressive unitary learning with non-Markovian interactions

Scaling-up current-era quantum processors would require better understanding of the underlying noise processes affecting the device. Although protocols like randomized benchmarking (RB) can help identify non-Markovian correlations in the device, they are often used only to obtain a single practical fidelity metric. We present a tomography approach for characterizing non-Markovian quantum dynamics through simple RB experiments. Our method focuses on learning the system-environment interaction by searching the unitary manifold using gradient-descent methods, solely guided by RB data. Through our approach, we learn the system-environment interaction unitary when Markovian and non-Markovian environments are simultaneously present.  We accurately estimate RB outputs for sequence lengths up to five times longer than utilized data with reconstruction fidelities exceeding 99\% and mean squared errors below $10^{-6}$. As an application of our work, we quantify leakage rates in exchange-only semiconductor qubits, a task crucial for enabling many quantum error correcting codes. Our work provides a readily deployable scalable framework for quantum system characterization, offering new capabilities for quantum error characterization and mitigation in realistic quantum hardware.