  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.
