Rapid Control of Quantum Systems: A Continuous Nonsmooth Function Based Approach

This paper addresses the critical objective of achieving rapid state transfer in quantum systems. Increasing control gain to achieve fast convergence can result in poor convergence. To circumvent this, a novel continuous, nonsmooth control is devised, exploiting Lyapunov conditions for quantum systems described by von Neumann equations. This approach ensures swift convergence to the target eigenstate while minimizing control effort and enhancing fidelity compared to prevalent techniques such as bang-bang control, approximate bang-bang control, and standard Lyapunov control. Several illustrative examples are provided to corroborate and validate the efficacy of the proposed methodology.