  Increasing the quantum information processing power with limited number of
hosts is vital for achieving quantum advantage. Here we propose a novel scheme
that achieves a scalable n-ion-2n-qubit quantum processor utilizing four
internal levels of each ion, and experimentally implement a 1-ion-2-qubit
universal processor using the valence electron spin and nuclear spin of a
single 171Yb+ ion. Fidelities of single-qubit and two-qubit gates are around
0.98 obtained by quantum process tomography. Additionally, the Grover's
algorithm is implemented with a successful rate exceeding 0.99. We provide
explicit scaling-up protocols based on standard laser-less and laser-based
frameworks, and further demonstrate that the electron/nuclear-spin scheme
allows less demanding two-qubit entangling gates between different ions. The
replacement of some inter-atomic gates by intra-atomic gates could increase the
fidelity of some quantum circuits. Our work paves the way towards achieving
2n-times increase in the size of quantum computational Hilbert space with n
ions.
