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

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