The column constraint requires an N queens placement to contain exactly one queen in every board column. With one queen already encoded per row, the oracle checks column occupancy alongside diagonal safety. section 8.3.1 section 8.2.2
In the Qiskit implementation, column checks accumulate queen indicators into validation qubits with controlled operations. A separate Python validator extracts each row’s queen column and rejects duplicate column indices. section 8.2.2 section 8.2.2
Figure 8.8 To check that no two queens share a column or a diagonal, we need to check each pair of rows separately. For each pair of rows, we calculate the difference of the indices of queens within them. This difference cannot be equal to zero or to the difference between the indices of these rows.
Compare each pair of rows by subtracting their queen-column indices; a zero difference identifies a shared column, while the row-distance comparison handles diagonal conflicts. section 8.3.1
