Fig. 1. Illustration for the communication types among quantum processing units

Fig. 2. Circuit for preparing Bell states (left) and their non-local representation (right)

Fig. 3. Circuit for preparing $\left|\mathrm{G}\mathrm{H}{\mathrm{Z}}_{\mathrm{3}}\right.〉$ state (left) and its non-local representation (right)

Fig. 4. Sketch circuit for quantum teleportation

Fig. 5. Sketch circuit for teleporting CNOT gate^[65]

Fig. 6. Circuit for entanglement swapping^[67]

Fig. 7. Sketch circuits of cat-entangler (left) and cat-disentangler (right)^[71]

Fig. 8. High-level system abstraction of the distributed quantum computing ecosystem^[50]

Fig. 9. Distributed three-qubit variational circuit^[120]

Fig. 10. Distributed Shor's algorithm^[121]

Fig. 11. Workflow of the modular quantum compilation framework for DQC architectures^[139]

Fig. 12. Illustrative circuit for wire cutting

Fig. 13. The "measure-and-prepare" channel^[140]

Fig. 14. Illustrative circuit for gate cutting

Fig. 15. Decomposition of two-qubit unitary ${\mathrm{e}}^{\mathrm{i}\theta A_{\mathrm{1}}\otimes A_{\mathrm{2}}}$ into a sequence of single-qubit gates^[141]

Fig. 16. Decomposition of CZ gate into a sequence of single-qubit gates^[141]

Fig. 17. Illustration of random Clifford circuit based circuit cutting method^[148]

Fig. 18. Sketch of wire cutting for a TTN-shaped quantum circuit^[160]

Fig. 19. Circuit cutting framework for quantum error mitigation^[161]