(color online) Energy levels, laser couplings, and the RRIs of (a) the control atom and (b) the target atoms used to construct the n-qubit controlled-phase gate. |R〉, |r〉 |a〉, and |b〉 denote the Rydberg states. |R〉₁|r〉_k → |b〉₁|a〉_k with defect δ₂ and strength V₂, and |r〉₁|R〉_k → |a〉₁|b〉_k with defect δ₁ and strength V₁. V_Rr is the strength of the dipole–dipole interaction between the control and target atoms. V_rr is the strength of the vdW interaction among the target atoms. The scheme requires V_Rr ≫ V_rr,^[69] which can be achieved by using Förster resonances and choosing suitable ℛ and n.^[73] The Rydberg state |a〉- and |b〉-induced transitions, as well as the vdW interactions V_rr give rise to the transition errors. Ω₁(k) is the Rabi frequency of the transitions |1〉 ↔ |R〉₁ (|1〉 ↔ |r〉_k) of control atom 1 (target atom k). |0〉 and |1〉 constitute the computation subspace.