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Parity-time (PT) symmetric non-Hermitian Hamiltonians bring about many novelfeatures and interesting applications such as quantum gates faster than thosein Hermitian systems, and topological state transfer. The performance ofevolutions under $\mathcal{PT}$-symmetric Hamiltonians is degraded by theinevitable noise and errors due to system-environment interaction andexperimental imperfections. In contrast to Hermitian Hamiltonians, thefluctuations in dissipative beams that are utilized to generate non-Hermitiancontributions in the PT-symmetric Hamiltonians cause additional errors. Here weachieve the protection of PT-symmetric Hamiltonians against noise acting alongthe qubit's quantization axis by combining quantum evolutions with dynamicaldecoupling sequences. We demonstrate the performance of our method by numericalsimulations. Realistic noise sources and parameters are chosen including:constant detuning error, time-varying detuning noise and dissipative-beamnoise. The fidelities of the protected evolutions are well above theunprotected ones under all the above situations. Our work paves the way forfurther studies and applications of non-Hermitian $\mathcal{PT}$-symmetricphysics in noisy quantum systems.

Protection of quantum evolutions under parity-time symmetric non-Hermitian Hamiltonians by dynamical decoupling