Fig. 1. Common gates of Clifford+T gate library. (a) NOT gate; (b) T gate; (c) CNOT gate

Fig. 2. Routing method. (a) SWAP gate; (b) Bridge gate

Fig. 3. Example of a quantum circuit

Fig. 4. Quantum chip coupling architecture

Fig. 5. ZX diagram representation of the quantum gate. (a) ZX diagram representation of CNOT gate; (b) ZX diagram representation of H gate; (c) ZX diagram representation of NOT gate; (d) ZX diagram representation of S gate;(e) ZX diagram representation of T gate; (f) ZX diagram representation of T⁺ gate

Fig. 6. Rewriting method of ZX diagram. (a) Rewriting method of target qubit; (b) Rewriting method of parameter gate; (c) Rewriting method of control qubit; (d) Rewriting method of reciprocal gate; (e) Rewriting method of adjacent H gate; (f) Rewriting method of merge CNOT gate

Fig. 7. Example circuit proof process for rule 1

Fig. 8. Example of the use of the exchange rule 1

Fig. 9. Example of the use of the exchange rule 2. (a) Example of exchanging gates with the same control bits;(b) Example of exchanging gates with the same target bits; (c) Example of exchanging gates with parallel gates

Fig. 10. Fixed layer circuit division method

Fig. 11. Three-layer dynamic circuit division method

Fig. 12. Mapping result of fig. 3 using the fixed layer division method

Fig. 13. Mapping process of the three-level circuit division method. (a) Example circuit initial division; (b) Using G₂ gate as a benchmark for initial circuit movement; (c) Routing example; (d) Mapping result

Fig. 14. Comparison of CNOT gates required