Entanglement-assisted circuit knitting: Distributed quantum computing using limited entanglement resources

Abstract

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 called entanglement-assisted circuit knitting that integrates these two paradigms by performing circuit knitting assisted with a limited amount of entanglement. We establish a general theoretical framework for entanglement-assisted circuit knitting. Optimal sampling overhead is achieved for Choi-stretchable unitaries with general entanglement resources, while for general unitaries we derive both lower and upper bounds for one-Bell-pair-assisted circuit knitting. We further extend the framework to the black-box setting, which can be treated as a class of quantum combs. This extension releases the need for explicit knowledge of the global unitary of a whole quantum circuit, enables a more flexible embedding structure, and broadens its applicability. Within this framework, we develop constructive protocols utilizing different resources, including entanglement, local operations, and classical communication. We derive the optimal mixed configuration among these protocols and provide an algorithm for its determination. Under dynamically probabilistic entanglement distribution, we reveal a trade-off between sampling overhead and entanglement cost in entanglement-assisted circuit knitting. This hybrid approach can thus be viewed as a form of hybrid classical-quantum computation, balancing sampling and entanglement efficiency, and enabling more resource-efficient implementations of distributed quantum computing.