  Quantum arithmetic circuits have practical applications in various quantum
algorithms. In this paper, we address quantum addition on 2-dimensional
nearest-neighbor architectures based on the work presented by Choi and Van
Meter (JETC 2012). To this end, we propose new circuit structures for some
basic blocks in the adder, and reduce communication overhead by adding
concurrency to consecutive blocks and also by parallel execution of expensive
Toffoli gates. The proposed optimizations reduce total depth from $140\sqrt
n+k_1$ to $92\sqrt n+k_2$ for constants $k_1,k_2$ and affect the computation
fidelity considerably.
