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Geometric quantum computation offers a practical strategy toward robustquantum computation due to its inherently error tolerance. However, therigorous geometric conditions lead to complex and/or error-disturbed quantumcontrols, especially for logical qubits that involve more physical qubits,whose error tolerance is effective in principle though, their experimentaldemonstration is still demanding. Thus, how to best simplify the needed controland manifest its full advantage has become the key to widespread applicationsof geometric quantum computation. Here we propose a new fast and robustgeometric scheme, with the decoherence-free-subspace encoding, and present itsphysical implementation on superconducting quantum circuits, where we onlyutilize the experimentally demonstrated parametrically tunable coupling toachieve high-fidelity geometric control over logical qubits. Numericalsimulation verifies that it can efficiently combine the error tolerance fromboth the geometric phase and logical-qubit encoding, displaying ourgate-performance superiority over the conventional dynamical one withoutencoding, in terms of both gate fidelity and robustness. Therefore, our schemecan consolidate both error suppression methods for logical-qubit control, whichsheds light on the future large-scale quantum computation.

Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource