Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis

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 Greenberger&#x2013;Horne&#x2013;Zeilinger (GHZ) states. These are prepared using ancillary qubits acting as an &#x201C;entanglement bus,&#x201D; unlocking global operation primitives such as multiqubit 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 a synthesis scheme for arbitrary Clifford operations requiring at most <inline-formula><tex-math notation="LaTeX">$2n+1$</tex-math></inline-formula> layers of entangled state injections, which can be computed classically in <inline-formula><tex-math notation="LaTeX">$O(n^{3})$</tex-math></inline-formula> time. In a square-lattice architecture with two entanglement buses, we show that a graph state can be synthesized using at most <inline-formula><tex-math notation="LaTeX">$\lceil \frac{1}{2}n\rceil +1$</tex-math></inline-formula> layers of GHZ state injections, and Clifford operations require only <inline-formula><tex-math notation="LaTeX">$\lceil \frac{3}{2} n \rceil + O(\sqrt{n})$</tex-math></inline-formula> layers of GHZ state injections.