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Besides the intrinsic noise resilience property, nonadiabatic geometricphases are of the fast evolution nature, and thus can naturally be used inconstructing quantum gates with excellent performance, i.e., the so-callednonadiabatic geometric quantum computation (NGQC). However, previoussingle-loop NGQC schemes are sensitive to the operational control error, i.e.,the $X$ error, due to the limitations of the implementation. Here, we propose arobust scheme for NGQC combining with the dynamical correction technique, whichstill uses only simplified pulses, and thus being experimental friendly. Wenumerically show that our scheme can greatly improve the gate robustness inprevious protocols, retaining the intrinsic merit of geometric phases.Furthermore, to fight against the dephasing noise, due to the $Z$ error, we canincorporate the decoherence-free subspace encoding strategy. In this way, ourscheme can be robust against both types of errors. Finally, we also propose howto implement the scheme with encoding on superconducting quantum circuits withexperimentally demonstrated technology. Therefore, due to the intrinsicrobustness, our scheme provides a promising alternation for the future scalablefault-tolerant quantum computation.

Robust nonadiabatic geometric quantum computation by dynamical correction