Electron transport in an assembly of ZnO quantum dots has been studied using an electrochemically gated transistor. The electron mobility shows a stepwise increase as a function of the electron occupation per quantum dot. When the occupation number is below two, transport occurs by tunneling between the S orbitals. Transport becomes 3 times faster when the occupation number is between two and eight; tunneling now occurs between the P orbitals. Electron transport is thus critically determined by the quantum properties of the building blocks.