On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

Understand

In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale.

• In previous works, the absence of traps for this problem was proven on various time scales.
• A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system.
• However, in the case of saddle the numbers of negative and positive eigenvalues of Hessian at this point and their magnitudes have not been studied.