Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries

The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with conventional capacitive coupled superconducting transmon qubits. A universal set of holonomic gates is constructed with the help of the interaction with an auxiliary qubit rather than relying on delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, which leads to high-fidelity gate operations. In this way, the distinct merit of our scheme is that we use only the lowest two levels of a transmon to form the qubit states. In addition, the auxiliary qubits are in their ground states before and after every gate operation, so that the holonomic gates can be constructed successively. Therefore, our scheme provides a promising method towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.