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Nonadiabatic geometric quantum computation in decoherence-free subspaces hasreceived increasing attention due to the merits of its high-speedimplementation and robustness against both control errors and decoherence.However, all the previous schemes in this direction have been based on theconventional geometric phases, of which the dynamical phases need to beremoved. In this paper, we put forward a scheme of nonadiabatic geometricquantum computation in decoherence-free subspaces based on unconventionalgeometric phases, of which the dynamical phases do not need to be removed.Specifically, by using three physical qubits undergoing collective dephasing toencode one logical qubit, we realize a universal set of geometric gatesnonadiabatically and unconventionally. Our scheme not only maintains all themerits of nonadiabatic geometric quantum computation in decoherence-freesubspaces, but also avoids the additional operations required in theconventional schemes to cancel the dynamical phases.

Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases