A 2D nearest-neighbor quantum architecture for factoring in polylogarithmic depth

We contribute a 2D nearest-neighbor quantum architecture for Shor’s algorithm to factor an n-bit number in O(log2(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.