1205.0036 (David Rosenbaum)

Optimal Quantum Circuits for Nearest-Neighbor Architectures    [PDF]

David Rosenbaum

We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the (k)D grid (\bbZ^k) where (k \geq 2) is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed. This allows minimum-depth circuits for the nearest-neighbor architecture to be obtained from minimum-depth circuits in the standard abstract model. Our work therefore justifies the standard assumption that quantum algorithms can perform interactions between arbitrary pairs of qubits. In particular, our results imply that Shor's algorithm, controlled operations and fan-outs can be implemented in constant depth, polynomial size and polynomial width in this architecture. We also present optimal non-adaptive quantum circuits for controlled operations and fan-outs on a (k)D grid. These circuits have depth (\Theta(\sqrt[k]{n})), size (\Theta(n)) and width (\Theta(n)). Our lower bound is for a general class of operations which includes controlled operations and fan-outs as special cases.

View original: http://arxiv.org/abs/1205.0036