Entanglement-assisted circuit knitting

TL;DR

This work addresses the challenge of scaling distributed quantum computation by reducing the sampling overhead of circuit knitting through limited entanglement. It introduces resource-assisted quasi-probability decomposition (QPD), unifying entanglement-assisted LOCC and classical circuit knitting into a single framework and extending it to black-box circuit knitting. The authors derive overhead bounds for wire cutting and gate cutting, showing that even a single Bell pair can reduce overhead toward the asymptotic limit of standard circuit knitting, and provide explicit bounds using fully entangled fractions and operator-Schmidt norms. They further extend the approach to black-box quantum combs, establishing lower bounds and, in favorable cases, tight overheads determined by the entanglement of resource states. Overall, the framework offers a principled, resource-aware path to practical, distributed quantum computation by balancing entanglement costs against sampling overhead, and it clarifies the trade-offs between classical information flow and quantum 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 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.

Figures (13)

• Figure 1: Schematic illustration of entanglement-assisted circuit knitting as a combination of entanglement-assisted LOCC and circuit knitting. Wiggly lines represent shared entanglement resources, while double lines denote classical communication. This framework achieves a balance between the amount of pre-shared entanglement and the resulting sampling overhead.
• Figure 2: (a) Resource-free QPD (b) Resource-assisted QPD
• Figure 3: Diagram of quantum state and gate teleportation. The blue one indicates the resource in the process, where the orange one indicates the free operation.
• Figure 4: Fully entanglement-assisted DQC. (a) Quantum state teleportation. (b) Quantum telegate implemented by entanglement-assisted LOCC Eisert2000.
• Figure 5: This figure illustrates two types of circuit knitting, namely wire cutting and gate cutting.

Theorems & Definitions (19)

• Definition 1: Quasi-probability decomposition over free maps
• Definition 2: Resource-assisted quasi-probability decomposition over free maps
• Definition 3
• Lemma 4
• Definition 5: Local unitary decomposition
• Proposition 6
• Lemma 7
• Corollary 8: Resource-assisted wire cutting Bechtold2024Bechtold2025
• Corollary 9
• theorem 10