A differentiable programming method for quantum control

Optimal control is highly desirable in many current quantum systems, especially to realize tasks in quantum information processing. We introduce a method based on differentiable programming to leverage explicit knowledge of the differential equations governing the dynamics of the system. In particular, a control agent is represented as a neural network that maps the state of the system at a given time to a control pulse. The parameters of this agent are optimized via gradient information obtained by direct differentiation through both the neural network and the differential equation of the system. This fully differentiable reinforcement learning approach ultimately yields time-dependent control parameters optimizing a desired figure of merit. We demonstrate the method's viability and robustness to noise in eigenstate preparation tasks for three systems: a single qubit, a chain of qubits, and a quantum parametric oscillator.