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Geometric phases are well known to be noise-resilient in quantumevolutions/operations. Holonomic quantum gates provide us with a robust waytowards universal quantum computation, as these quantum gates are actuallyinduced by nonabelian geometric phases. Here we propose and elaborate how toefficiently implement universal nonadiabatic holonomic quantum gates on simplersuperconducting circuits, with a single transmon serving as a qubit. In ourproposal, an arbitrary single-qubit holonomic gate can be realized in asingle-loop scenario, by varying the amplitudes and phase difference of twomicrowave fields resonantly coupled to a transmon, while nontrivial two-qubitholonomic gates may be generated with a transmission-line resonator beingsimultaneously coupled to the two target transmons in an effective resonantway. Moreover, our scenario may readily be scaled up to a two-dimensionallattice configuration, which is able to support large scalable quantumcomputation, paving the way for practically implementing universal nonadiabaticholonomic quantum computation with superconducting circuits.

Implementing universal nonadiabatic holonomic quantum gates with transmons