The control of quantum bits (qubits) remains a major challenge due to the destructive effects of environmental noise, which limits the reliability of quantum computation. Riccardo Cantone, Shreyasi Mukherjee, Luigi Giannelli and a team of researchers from the University of Catania and the National Institute of Physics and Nuclear Research are tackling this problem by developing a new control strategy that intelligently combines the power of established physics-based modeling and machine learning. An innovative approach that uses neural networks trained on simulated data effectively accounts for complex and non-standard noise patterns and achieves very high gating fidelity of >90% even under difficult noise conditions. This advance represents an important step toward building more robust and practical quantum technology, paving the way for more complex and reliable quantum algorithms.
Researchers apply a machine learning-enhanced gray-box framework to quantum-optimal control protocols designed for open quantum systems. This approach combines a white-box physical model with a black-box neural network trained using synthetic data. This method effectively captures non-Markov noise effects and achieves gate fidelity greater than 90% when subjected to random telegraph noise and Ornstein-Uhlenbeck noise. This research addresses key issues in maintaining the performance of quantum information processing.
Neural networks enhance quantum control of qubits
Introduction In this study, we present an attention-based machine learning-enhanced gray-box framework for quantum optimal control, designed to improve the operation of open quantum systems subject to complex noise. Quantum control is essential for technologies such as computing, communications, and sensing, but robust control is difficult to achieve when systems interact with non-Markov environments that are difficult to characterize. The proposed grey-box model combines a white-box component that captures analytically tractable system dynamics using known physical principles, and a black-box component implemented via a neural network trained to learn from data about unmodeled environmental influences. The model was tested using synthetic data applied to a purely out-of-phase qubit, accounting for both random telegraph noise (RTN) and Ornstein-Uhlenbeck (OU) noise. System and model In this study, we consider a single qubit that is affected by classical out-of-phase noise along the z-axis, driven by an external control field.
In the interaction diagram, the dynamics are described by the time-dependent Hamiltonian H
Since the latter is Gaussian distributed while the former is not, the stochastic process is different and affects dynamic protocols for protection against noise such as spin echoes. Machine Learning Model The proposed grey-box model integrates analytical knowledge of quantum systems with transformer-based neural networks. This hybrid architecture includes a white-box part that enforces the known unitary dynamics of the driving qubit and associated measurement process, and a black-box neural network trained to model the influence of the environment on the evolution of the system. The model takes as input the amplitude of five Gaussian-controlled pulses applied along each of the x- and y-axes, yielding a total of 10 real parameters, while the pulse width and position are fixed. The output consists of six gate fidelity, each associated with a different target from a universal set of single-qubit gates. The black-box core is a lightweight transformer encoder that processes input pulse parameters and predicts a set of noise-related parameters that are fed to a white-box layer that implements Hamiltonian construction, time evolution based on a discretized control field, expectation computation for a tomographically complete set of initial states, and process matrix reconstruction and fidelity estimation.
Only the black-box layer contains trainable parameters, and the network is trained using the Adam optimizer to minimize the mean squared error across six prediction fidelity. Training is supervised and based on synthetic data generated by simulating noisy quantum dynamics using white-box constraints that ensure physically consistent predictions. Results and Open Issues Separate models are trained over different values of the coupling strength g, providing insight into the effectiveness of the grey-box approach as a function of the markovianity (parameterized by the g/γ ratio) of the quantum map describing its time evolution under the influence of noise. For RTN, the model had low training and testing mean squared errors across all gates, and prediction errors increased with g but remained in the 10-2, 10-3 range, indicating robust generalization. As an emulator of optimal control pipelines, we are now able to design control pulses that achieve >99% fidelity at minimum g and >90% at maximum g, with only small gate-dependent variations.
The OU case showed similar performance, with low and stable mean squared error values across all g, confirming its robustness to different noise types. The best control results mirrored the RTN case, with fidelity above 99% at low g and remaining above 90% at stronger couplings. Although fidelity decreases with higher noise, the model continues to support effective pulse design, and future improvements may benefit from larger datasets and more advanced strategies. The results validate the gray-box approach and show that the optimization framework is effective at suppressing the effects of low-frequency noise (g/γ 1), but less effective against the noise that generates Markov maps (g/γ 1).
Gray box control beyond noise limits
Scientists have developed a grey-box framework that combines physical modeling and neural networks to achieve high-fidelity control of open quantum systems even in the presence of difficult noise conditions. This innovative approach effectively captures non-Markov noise effects, a major hurdle in quantum computing, and achieves significant improvements in gate fidelity. The team trained a neural network using synthetic data constrained by a white-box physical model to ensure physically valid predictions, and then used this model within an optimal control protocol. Experimental results revealed that the trained model exhibited low mean squared error across all gates tested, with prediction errors consistently staying within the range of 10-2 to 10-3, demonstrating robust generalization capabilities. By utilizing this model as an emulator, the scientists achieved gating fidelity of >99% at the lowest binding strengths and maintained >90% fidelity at the highest binding strengths tested.
These results demonstrate the framework's ability to design control pulses that effectively reduce the effects of noise on quantum operations. Further investigation of different types of noise, particularly random telegraph noise and Ornstein-Uhlenbeck noise, confirmed the robustness and consistent performance of the model. Measurements confirm that the optimization framework is particularly effective in suppressing the effects of low-frequency noise when the ratio of coupling strength to noise strength (g/γ) is greater than 1. However, studies have shown that the effectiveness of noise-generated Markov maps decreases when g/γ is less than 1, suggesting a delicate relationship between noise characteristics and control performance. This breakthrough provides a powerful tool to improve the reliability and accuracy of quantum computation, paving the way to more complex and robust quantum systems.
