Nonperturbative Leakage Elimination Operator-Based Quantum Control Pulse Design Beyond the High Frequency Driving Regime

Abstract

Precise quantum pulse design is central to achieving high precision quantum control, while level leakage induced by system environment coupling is the bottleneck limiting control precision. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from target subspace to other leakage spaces. The analytical control conditions under the high frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, low frequency driving is experimentally more feasible, and the driving strength is subject to a fundamental physical bound. In this work, we overcome the high frequency driving limit in the pulse design by recasting the LEO protocol within the nonperturbative Floquet-Magnus framework. Applying the Magnus expansion to Floquet dynamical localization, we establish a generalized optimal control formalism that is applicable to the low frequency regime. We prove that the analytical control conditions derived via the Feshbach PQ partitioning technique are equivalent to the zero order Magnus expansion, and that higher order Magnus terms must be taken into account in the low frequency driving regime. We validate our nonperturbative framework using two examples: near perfect quantum state transfer in a one dimensional spin chain and adiabatic speedup in a two level system, corresponding to time independent and time dependent system Hamiltonians, respectively. Our results provide an effective route for designing control pulses in the low frequency regime, which is promising for practical quantum information processing tasks across diverse experimental platforms, including superconducting qubits and ion traps.