  Geometric quantum computation offers a practical strategy toward robust
quantum computation due to its inherently error tolerance. However, the
rigorous geometric conditions lead to complex and/or error-disturbed quantum
controls, especially for logical qubits that involve more physical qubits,
whose error tolerance is effective in principle though, their experimental
demonstration is still demanding. Thus, how to best simplify the needed control
and manifest its full advantage has become the key to widespread applications
of geometric quantum computation. Here we propose a new fast and robust
geometric scheme, with the decoherence-free-subspace encoding, and present its
physical implementation on superconducting quantum circuits, where we only
utilize the experimentally demonstrated parametrically tunable coupling to
achieve high-fidelity geometric control over logical qubits. Numerical
simulation verifies that it can efficiently combine the error tolerance from
both the geometric phase and logical-qubit encoding, displaying our
gate-performance superiority over the conventional dynamical one without
encoding, in terms of both gate fidelity and robustness. Therefore, our scheme
can consolidate both error suppression methods for logical-qubit control, which
sheds light on the future large-scale quantum computation.
