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Two-level-system (TLS) defects in amorphous dielectrics are a major source ofnoise and decoherence in solid-state qubits. Gate-dependent non-Markovianerrors caused by TLS-qubit coupling are detrimental to fault-tolerant quantumcomputation and have not been rigorously treated in the existing literature. Inthis work, we derive the non-Markovian dynamics between TLS and qubits during aSWAP-like two-qubit gate and the associated average gate fidelity forfrequency-tunable Transmon qubits. This gate dependent error model facilitatesusing qubits as sensors to simultaneously learn practical imperfections in boththe qubit's environment and control waveforms. We combine the-state-of-artmachine learning algorithm with Moir\'{e}-enhanced swap spectroscopy to achieverobust learning using noisy experimental data. Deep neural networks are used torepresent the functional map from experimental data to TLS parameters and aretrained through an evolutionary algorithm. Our method achieves the highestlearning efficiency and robustness against experimental imperfections to-date,representing an important step towards in-situ quantum control optimizationover environmental and control defects.

Learning Non-Markovian Quantum Noise from Moir\'{e}-Enhanced Swap Spectroscopy with Deep Evolutionary Algorithm