Gate Teleportation vs Circuit Cutting in Distributed Quantum Computing

Distributing circuits across quantum processor modules will enable the execution of circuits larger than the qubit count limitations of monolithic processors. While distributed quantum computation has primarily utilized circuit cutting, it incurs an exponential growth of sub-circuit sampling and classical post-processing overhead with an increasing number of cuts. The entanglement-based gate teleportation approach does not inherently incur exponential sampling overhead, provided that quantum interconnects of requisite performance are available for generating high-fidelity Bell pairs. Recent advances in photonic entanglement of qubits have motivated discussion on optical link metrics required to achieve remote gate performance approaching circuit-cutting techniques. We model noisy remote (teleported) gates between superconducting qubits entangled via noisy microwave-to-optical (M2O) transducers over optical links. We incorporate the effect of the transducer noise added $N_add$ on the Bell pair fidelity and inject noisy Bell pairs into remote CNOT gates. We perform a comparative simulation of Greenberger-Horne-Zeilinger (GHZ) states generated between processor modules using remote gates and gate cuts by studying the dependence of the Hellinger fidelity on the primary source of error for the two approaches. We identify break-even points where noisy remote gates achieve parity with gate-cuts. Our work suggests that a 10-fold reduction in the present M2O transducer noise added figures would favor generating multipartite entangled states with remote gates over circuit cutting due to an exponential sampling overhead for the latter. Our work informs near-term quantum interconnect hardware metrics and motivates a network-aware hybrid quantum-classical distributed computation approach, where both quantum links and circuit cuts are employed to minimize quantum runtime.