Pulse-Level Quantum Robust Control with Diffusion-Based Reinforcement Learning

The pulse-level quantum control presents a large range of external parameter dependencies, including control field noise, frequency detuning, nonlinearities, and uncertainty of Hamiltonian parameters, which can lead to significant deviation from the target quantum gate. These terms are not usually considered directly in standard optimization scenarios for robustness, but are often found in analytical solutions. The latter are often difficult to emerge and generalize to different settings. This paper proposes a diffusion-based reinforcement learning method for pulse-level quantum robust control (PQC-DBRL) to enhance the robustness of pulse-level quantum gate control. PQC-DBRL does not require an accurate Hamiltonian model of the underlying system, effectively mitigating deviations from target quantum gates caused by control field noise and parameter uncertainties. The quantum pulse control problem is formulated as a conditional generative modeling task, leveraging diffusion reinforcement learning to capture unobserved system information. Furthermore, the results show that PQC-DBRL pulses maintain a fidelity greater than 0.95 for 100% of the cases and greater than 0.999 for 32.16% of the cases, outperforming GRAPE, which achieves 0.999 fidelity for only 12.48% of the cases under the same noise conditions. In large-scale experiments with repeated gate operations, PQC-DBRL demonstrates significantly higher resilience to cumulative errors, maintaining fidelity advantages even after 200 gate repetitions. Additionally, when evaluated across different Hamiltonian variations, PQC-DBRL shows smaller fidelity variance compared to GRAPE, indicating higher robustness against system parameter fluctuations. This paper offers a promising solution to scalable, noise-resilient quantum control in practical quantum computing applications.