Circuit knitting facing exponential sampling-overhead scaling bounded by entanglement cost
Mingrui Jing, Chengkai Zhu, Xin Wang · Physical Review A · 2025
Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even with the asymptotic amount of resources using the parallel cut strategy. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we develop the faithful lower bounds for the regularized sampling overhead based on channels' $\ensuremath{\kappa}$ entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasiprobability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.