Coherent control of motional quanta for a three-qubit encoding in neutral ytterbium-171 atoms

We present an architecture for encoding three qubits within the optical "clock" transition, nuclear spin, and motional degrees of freedom of ytterbium-171 atoms in optical tweezers. This architecture extends the two-qubit "ququart" encoding from previous work to give greater hardware efficiency for the purposes of quantum computation and simulation. We present a set of native implementations of several one-, two-, and three-qubit gates that can be performed within the "quoct" space of a single atom, three- and four-qubit Rydberg gates between atoms, and a state measurement protocol leveraging coherent control of motional quanta both inside and outside the computational basis. We demonstrate the advantages of this encoding with an implementation of a quantum chromodynamics simulation in 1+1D for a single flavor of quark in the axial gauge.