Control Optimization Landscape Analysis of Interacting Quantum Systems*

Fine-tuning quantum processors is labor-intensive, typically relying on intricate experimental approaches, complicated models, and computationally intensive simulations. Constraints of computational resources restrict existing methods from simultaneously calibrating individual quantum gates. Consequently, sequential gate calibration techniques typically neglect the impact of undesired crosstalk and system interactions and, thus, limit the performance of simultaneous gate operations. These interactions and interferences between discrete components of quantum processors and control signals represent a substantial obstacle in calibrating ever-larger quantum information processors. Here, we numerically investigate the effects of quantum interactions on quantum gate optimization, particularly its optimization landscape. Prior research has shown that under ideal assumptions, such as controllability, almost all closed, finite-dimensional quantum systems have trap-free optimization landscapes, meaning, during gate calibration, the global optimum is almost always reached. We explore how the suboptimal nature of optimization landscapes changes based on the selection of the loss function and the undesired strengths of interactions between qubits. Identifying limits on interaction strengths can inform the feasibility of simultaneous gate calibration routines and thus significantly reduce the calibration effort.