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 for asymptotic overhead in the parallel cut regime. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication (LOCC), of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we show that the regularized sampling overhead for simulating a general bipartite channel via LOCC is lower bounded by $\kappa$-entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasi-probability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.

翻译：电路编织是一种跨多个处理器连接量子电路以模拟非局域量子操作的方法，是分布式量子计算中一种具有前景的技术。尽管目前已发展出多种电路编织技术，但我们揭示了该技术可扩展性的根本局限。我们证明：即使考虑并行切割区域中的渐近开销，电路编织的采样开销仍受目标二分体动力学精确纠缠成本的指数级下限约束。具体而言，我们证明：在局域操作与经典通信（LOCC）辅助下，任意二分量子信道的正则化采样开销受可分保序操作下其精确纠缠成本的指数级下限约束。此外，我们证明通过LOCC模拟一般二分信道时，正则化采样开销存在κ-纠缠与最大Rains信息的下界，从而提供了可高效计算的基准。本工作揭示了基于准概率分解的虚拟量子信息处理与量子香农理论之间的深刻关联，凸显了纠缠在分布式量子计算中的关键作用。