Engineering Nonequilibrium Steady States via Quantum Optimal Control

Dissipative quantum systems under periodic drive evolve into nonequilibrium steady states (NESSs) after the initial transients, where quantum states still evolve in time but the stroboscopic states – observing the quantum systems at the integer multiples of the drive period – are constant. Our previous work demonstrated Floquet drive as a versatile tool to stabilize a single dissipative qubit at various high-purity NESSs. In this presentation, I will talk about our recent work on applying quantum optimal control theory to optimize the Floquet drive applied to dissipative quantum systems. We implement a gradient-based optimizer that differentiates the Floquet propagator with respect to control parameters, enabling efficient numerical optimization of the purity of NESSs. Using this method, we further study stabilizing two-qubit entangled states when dissipation is present. Our study opens new avenues to harness dissipation engineering and optimal control theory in quantum technologies.