  Quantum gates, which are the essential building blocks of quantum computers,
are very fragile. Thus, to realize robust quantum gates with high fidelity is
the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic
geometric quantum computation scheme on superconducting circuits to engineer
arbitrary quantum gates, which share both the robust merit of geometric phases
and the capacity to combine with optimal control technique to further enhance
the gate robustness. Specifically, in our proposal, arbitrary geometric
single-qubit gates can be realized on a transmon qubit, by a resonant microwave
field driving, with both the amplitude and phase of the driving being
time-dependent. Meanwhile, nontrivial two-qubit geometric gates can be
implemented by two capacitively coupled transmon qubits, with one of the
transmon qubits' frequency being modulated to obtain effective resonant
coupling between them. Therefore, our scheme provides a promising step towards
fault-tolerant solid-state quantum computation.
