Protected quantum gates using qubit doublons in dynamical optical lattices

Quantum computing represents a central challenge in modern science. Neutral atoms in optical lattices have emerged as a leading computing platform, with collisional gates offering a stable mechanism for quantum logic. However, previous experiments have treated ultracold collisions as a dynamically fine-tuned process, which obscures the underlying quantum- geometry and statistics crucial for realising intrinsically robust operations. Here, we propose and experimentally demonstrate a purely geometric two-qubit swap gate by transiently populating qubit doublon states of fermionic atoms in a dynamical optical lattice. The presence of these doublon states, together with fermionic exchange anti-symmetry, enables a two-particle quantum holonomy -- a geometric evolution where dynamical phases are absent. This yields a gate mechanism that is intrinsically protected against fluctuations and inhomogeneities of the confining potentials. The resilience of the gate is further reinforced by time-reversal and chiral symmetries of the Hamiltonian. We experimentally validate this exceptional protection, achieving a loss-corrected amplitude fidelity of $99.91(7)\%$ measured across the entire system consisting of more than $17'000$ atom pairs. When combined with recently developed topological pumping methods for atom transport, our results pave the way for large-scale, highly connected quantum processors. This work introduces a new paradigm for quantum logic, transforming fundamental symmetries and quantum statistics into a powerful resource for fault-tolerant computation.