  We use a co-trapped ion ($^{88}\mathrm{Sr}^{+}$) to sympathetically cool and
measure the quantum state populations of a memory-qubit ion of a different
atomic species ($^{40}\mathrm{Ca}^{+}$) in a cryogenic, surface-electrode ion
trap. Due in part to the low motional heating rate demonstrated here, the state
populations of the memory ion can be transferred to the auxiliary ion by using
the shared motion as a quantum state bus and measured with an average accuracy
of 96(1)%. This scheme can be used in quantum information processors to reduce
photon-scattering-induced error in unmeasured memory qubits.
