  The nonadiabatic geometric quantum computation is promising as it is robust
against certain types of local noises. However, its experimental implementation
is challenging due to the need of complex control on multi-level and/or
multiple quantum systems. Here, we propose to implement it on a two-dimensional
square superconducting qubit lattice. In the construction of our geometric
quantum gates, we only use the simplest and experimentally accessible control
over the qubit states of the involved quantum systems, without introducing any
auxiliary state. Specifically, our scheme is achieved by parametrically tunable
all-resonant interaction, which leads to high-fidelity quantum gates.
Meanwhile, this simple implementation can be conveniently generalized to a
composite scenario, which can further suppress the systematic error during the
gate operations. In addition, universal nonadiabatic geometric quantum gates in
decoherence-free subspace can also be realized based on the tunable coupling
between only two transmon qubits, without consulting to multiple qubits and
only using two physical qubits to encode a logical qubit. Therefore, our
proposal provides a promising way of high-fidelity geometric manipulation for
robust solid-state quantum computation.
