  In superconducting architectures, limited connectivity remains a significant
challenge for the synthesis and compilation of quantum circuits. We consider
models of entanglement-assisted computation where long-range operations are
achieved through injections of large GHZ states. These are prepared using
ancillary qubits acting as an ``entanglement bus,'' unlocking global operation
primitives such as multi-qubit Pauli rotations and fan out gates. We derive
bounds on the circuit size for several well studied problems, such as CZ
circuit, CX circuit, and Clifford circuit synthesis. In particular, in an
architecture using one such entanglement bus, we give an $O(n^3)$-complexity
synthesis scheme for arbitrary Clifford operations requiring at most $2n + 1$
layers of entangled-state-injections. In a square-lattice architecture with two
entanglement buses, we show that a graph state can be synthesized using at most
$\lceil \frac{1}{2}n \rceil + 1$ layers of GHZ state injections, and Clifford
operations require only $\lceil\frac{3}{2} n \rceil + O(\sqrt n)$ layers of GHZ
state injections.
