Quantum Register of Fermion Pairs*

Quantum control of motion enables protocols to process and distribute quantum information and allows probing entanglement in correlated states of matter. However, motional coherence of individual particles can be fragile to maintain. Systems in nature with robust motional coherence instead often involve pairs of particles, such as Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, only dependent on mass and lattice wavelength. We observe quantum coherence beyond ten seconds. Modulating interactions between the atoms provides universal control of the motional qubit. The methods presented here open the door towards coherently programmable quantum simulators of many-fermion systems, and, by implementing further advances, digital quantum computation employing fermion pairs.