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In this work, we propose an adder for the 2D NTC architecture, designed tomatch the architectural constraints of many quantum computing technologies. Thechosen architecture allows the layout of logical qubits in two dimensions andthe concurrent execution of one- and two-qubit gates with nearest-neighborinteraction only. The proposed adder works in three phases. In the first phase,the first column generates the summation output and the other columns do thecarry-lookahead operations. In the second phase, these intermediate values arepropagated from column to column, preparing for computation of the final carryfor each register position. In the last phase, each column, except the firstone, generates the summation output using this column-level carry. The depthand the number of qubits of the proposed adder are $\Theta(\sqrt{n})$ and O(n),respectively. The proposed adder executes faster than the adders designed forthe 1D NTC architecture when the length of the input registers $n$ is largerthan 58.

An $\Theta(\sqrt{n})$-depth Quantum Adder on a 2D NTC Quantum Computer Architecture