A quantum register using collective excitations in an atomic ensemble without a Rydberg blockade

A qubit made up of an ensemble of atoms is attractive due to its resistance to atom losses, and many proposals to realize such a qubit are based on the Rydberg blockade effect. Here, we instead consider an experimentally feasible protocol to coherently load a 3D spin-dependent optical lattice from a spatially overlapping Bose--Einstein condensate. Identifying each lattice site as a qubit, with an empty or filled site as the qubit basis, we discuss how high-fidelity single-qubit operations, two-qubit gates between arbitrary pairs of qubits, and nondestructive measurements could be performed. In this setup, the effect of atom losses has been mitigated, and at no point do we need to remove the atoms from the computational basis in the ground state manifold, both of which can be significant sources of decoherence in other types of atomic qubits. Finally, we explore how one could also use the condensate as either a spectator to continuously measure and calibrate the laser and magnetic fields controlling the qubits, or as a tool to address individual qubits in the lattice by imprinting topological defects in the condensate without the typical need for mutliple tightly focused laser beams.