Evolution-Level Quantum Optimal Control of Single-Qubit Gates with Physics-Informed Neural Networks

Traditional quantum optimal control typically treats gate design as a pulse-shaping problem, where a sequence of discrete pulse amplitudes is optimized to achieve a target unitary operation. This paper proposes a paradigm shift by modeling the entire gate-forming process as a continuous, differentiable dynamical system. By using physics-informed neural networks (PINNs), the authors represent control fields and state trajectories as continuous functions of time. The Bloch equation is embedded directly into the optimization objective, ensuring that the learned control fields and trajectories are physically consistent throughout the evolution.

• Unified Optimization: The framework treats the total gate duration as a trainable parameter alongside the control fields, allowing the system to naturally settle on an optimal time scale without requiring an external duration scan.
• Physical Interpretability: Because the representation is continuous and differentiable, the internal structure of the controlled evolution is accessible. This allows researchers to inspect how the gate is physically constructed, rather than treating the control process as a black box.
• Diagnostic Feedback: For geometric gates, the model identifies localized regions along the trajectory where the geometric condition is poorly maintained. This diagnosis is fed back into the training process, allowing for targeted refinement of the control fields to reduce residual errors while maintaining high fidelity.

In experimental quantum computing, high-fidelity gate design must account for hardware-specific constraints and local variations. By moving from a discrete pulse-level view to a process-level view, this method provides a more flexible and physically transparent way to design gates. It enables the systematic adaptation of controls to specific experimental environments, making optimized quantum operations more robust and easier to calibrate in practice.