  We contribute a 2D nearest-neighbor quantum architecture for Shor's algorithm
to factor an $n$-bit number in $O(\log^2(n))$ depth. Our implementation uses
parallel phase estimation, constant-depth fanout and teleportation, and
constant-depth carry-save modular addition. We derive upper bounds on the
circuit resources of our architecture under a new 2D nearest-neighbor model
which allows a classical controller and parallel, communicating modules. We
also contribute a novel constant-depth circuit for unbounded quantum unfanout
in our new model. Finally, we provide a comparison to all previous
nearest-neighbor factoring implementations. Our circuit results in an
exponential improvement in nearest-neighbor circuit depth at the cost of a
polynomial increase in circuit size and width.
