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In the era of Noisy Intermediate-Scale Quantum computing as well as in error correcting circuits, physical qubits coherence time and high fidelity gates are essential to the functioning of quantum computers. In this paper, we demonstrate theoretically and experimentally, that pulses designed by optimization can be used to counteract the loss of fidelity due to a control amplitude error of the transmon qubit. We analyze the control landscape obtained by robust optimal control and find it to depend on the error range, namely the solutions can get trapped in the basin of attraction of sub-optimal solutions. Robust controls are found for different error values and are compared to an incoherent loss of fidelity mechanism due to a finite relaxation rate. The controls are tested on the IBMQ's qubit and found to demonstrate resilience against significant 10\% errors.
Cykiert et al. (Sat,) studied this question.