• Chinese Journal of Quantum Electronics
  • Vol. 42, Issue 1, 136 (2025)
JIANG Yibo, CHEN Zilu, CHENG Xueyun*, and GUAN Zhijin
Author Affiliations
  • School of Information Science and Technology, Nantong University, Nantong 226019, China
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    DOI: 10.3969/j.issn.1007-5461.2025.01.013 Cite this Article
    Yibo JIANG, Zilu CHEN, Xueyun CHENG, Zhijin GUAN. Quantum circuit mapping method based on dynamic circuit division and gate sequence recombination[J]. Chinese Journal of Quantum Electronics, 2025, 42(1): 136 Copy Citation Text show less
    Common gates of Clifford+T gate library. (a) NOT gate; (b) T gate; (c) CNOT gate
    Fig. 1. Common gates of Clifford+T gate library. (a) NOT gate; (b) T gate; (c) CNOT gate
    Routing method. (a) SWAP gate; (b) Bridge gate
    Fig. 2. Routing method. (a) SWAP gate; (b) Bridge gate
    Example of a quantum circuit
    Fig. 3. Example of a quantum circuit
    Quantum chip coupling architecture
    Fig. 4. Quantum chip coupling architecture
    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. 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
    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. 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
    Example circuit proof process for rule 1
    Fig. 7. Example circuit proof process for rule 1
    Example of the use of the exchange rule 1
    Fig. 8. Example of the use of the exchange rule 1
    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. 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
    Fixed layer circuit division method
    Fig. 10. Fixed layer circuit division method
    Three-layer dynamic circuit division method
    Fig. 11. Three-layer dynamic circuit division method
    Mapping result of fig. 3 using the fixed layer division method
    Fig. 12. Mapping result of fig. 3 using the fixed layer division method
    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. 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
    Comparison of CNOT gates required
    Fig. 14. Comparison of CNOT gates required

    算法1: 基于线路动态划分与门序重组的量子线路映射算法

    输入:

    逻辑量子线路L, 耦合架构G(V, E), 距离矩阵D_M, 交换规则E_R

    输出:

    新的映射线路P, 额外插入的CNOT门数C

    1.

    Begin

    2.

      R ←[] // 初始化路由方式列表

    3.

      i = j = k = 0 // 初始化下标

    4.

      While i<len(L) do

    5.

        If L[i] not match G then // 线路动态划分

    6.

          (M,N,E)=Divide_circuit(L[i])

    7.

        Else i++

    8.

        Dlen(E) // 根据拓展层长度确定移动窗口大小

    9.

        While j<D do

    10.

          If E[j] match G and E_R then

    11.

            M=Gate_remove(E[j]) // 门序移动

    12.

          Else j++

    13.

        End

    14.

        Forech k in R do

    15.

          Route = Cost_function(R[k])min // 选择路由代价最小的方式

    16.

        Mapping(N, Route, mapping, G) // 线路映射

    17.

        End

    18.

        Return P and C

    19.

    End

    Table 0. [in Chinese]
    Item Original circuitHA schemeProposed schemeOptimization rate
    NamenGatenumCNOTnumCNOTnumΔCNOTnum/%
    decod24-v2_43522332718
    4gt5_75538604230
    4gt13_91549605410
    4gt13_9055354540
    alu-v4_36551695717
    hwb4_49510717113819
    Table 1. Comparative experimental result of quantum circuits on the ibm_quito architecture
    Original CircuitHA schemeProposed schemeOptimization Rate
    NamenGatenumCNOTnumCNOTnumΔCNOTnum /%
    4gt5_75538605410
    decod24-v2_43522330
    rd73_2521053216162423631
    sym9_1481021504240031901121
    life_2381122445275431902331
    z4_2681130733603196246
    sqrt8_2601230093789231339
    cycle10_2_1101260504485312030
    adr4_1971334394608311132
    cm42a_20714177617311803-4
    cm85a_2091411414147181023330
    dc2_22215946212336822333
    col14_2151517936177871202732
    inc_237161061976238013-5
    mlp4_2451618852243121702230
    Table 2. Comparative experimental result of quantum circuits on the ibm_washington architecture
    Yibo JIANG, Zilu CHEN, Xueyun CHENG, Zhijin GUAN. Quantum circuit mapping method based on dynamic circuit division and gate sequence recombination[J]. Chinese Journal of Quantum Electronics, 2025, 42(1): 136
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