Entanglement-assisted circuit knitting

Distributed quantum computing (DQC) provides a promising route toward scalable quantum computation, where entanglement-assisted LOCC and circuit knitting represent two complementary approaches. The former deterministically realizes nonlocal operations but demands extensive entanglement resources, whereas the latter requires no entanglement yet suffers from exponential sampling overhead. Here, we propose a hybrid framework that integrates these two paradigms by performing circuit knitting assisted with a limited amount of entanglement. We establish a general theoretical formulation that yields lower bounds on the optimal sampling overhead and present a constructive protocol demonstrating that a single shared Bell pair can reduce the overhead to the asymptotic limit of standard circuit knitting without requiring classical communication. Furthermore, we extend the entanglement-assisted circuit knitting framework to the black-box setting, which can be applicable to the circuit knitting of quantum combs. This hybrid approach can be viewed as a form of hybrid classical-quantum computation, balancing the trade-off between sampling and entanglement efficiency, and enabling more resource-practical implementations of distributed quantum computing.