Improved Synthesis of Clifford Circuits using Long-Range CAT States

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 entangled CAT 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 show that Clifford operations require at most $2n+1$ layers of entangled-state-injections, significantly improving upon the best known SWAP-based approaches which achieve an entangling-gate-depth of $7n-4$. 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 CAT state injections, and Clifford operations require only $\lceil\frac{3}{2} n \rceil+ O(\sqrt n)$ layers of CAT state injections.