Quantum optimal control using physics-informed neural networks with sinusoidal representations.

Quantum gates on some quantum technologies, such as superconducting qubits, require carefully shaped pulses for high-fidelity operation. Algorithms like GRAPE and CRAB can discover these fine-tuned pulses but can require extensive optimization and run-time. As an alternative, we explore the use of physics-informed neural networks (PINNs) for quantum optimal control. Our PINN is a feedforward neural network whose loss function includes terms that enforce the Schrödinger equation, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We adopt ideas from the Sinusoidal Representation Network (SIREN) for weight initialization and sinusoidal activation function. We apply the model and discover high-fidelity gate pulses for quantum operations like QFT, CNOT, Hadamard, etc. Compared to CRAB and GRAPE, PINN yields comparable and higher fidelities for many gates. Our ultimate goal is a generalizable model that adapts to various quantum systems without retraining and outperforms existing algorithms.