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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.06986 |
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| _version_ | 1866911793086988288 |
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| author | Ni, Xiao-Hui Cai, Bin-Bin Liu, Hai-Ling Qin, Su-Juan Gao, Fei Wen, Qiao-Yan |
| author_facet | Ni, Xiao-Hui Cai, Bin-Bin Liu, Hai-Ling Qin, Su-Juan Gao, Fei Wen, Qiao-Yan |
| contents | Recently, Zhou et al. have proposed a novel Interpolation-based (INTERP) strategy to generate the initial parameters for the Parameterized Quantum Circuit (PQC) in Quantum Approximate Optimization Algorithm (QAOA). INTERP produces the guess of the initial parameters at level $i+1$ by applying linear interpolation to the optimized parameters at level $i$, achieving better performance than random initialization (RI). Nevertheless, INTERP consumes extensive running costs for deep QAOA because it necessitates optimization at each level of the PQC. To address this problem, a Multilevel Leapfrogging Interpolation (MLI) strategy is proposed. MLI can produce the guess of the initial parameters from level $i+1$ to $i+l$ ($l>1$) at level $i$, omitting the optimization rounds from level $i+1$ to $(i+l-1)$. The final result is that MLI executes optimization at few levels rather than each level, and this operation is referred to as Multilevel Leapfrogging optimization (M-Leap). The performance of MLI is investigated on the Maxcut problem. Compared with INTERP, MLI reduces most optimization rounds. Remarkably, the simulation results demonstrate that MLI can achieve the same quasi-optima as INTERP while consuming only 1/2 of the running costs required by INTERP. In addition, for MLI, where there is no RI except for level $1$, the greedy-MLI strategy is presented. The simulation results suggest that greedy-MLI has better stability (i.e., a higher average approximation ratio) than INTERP and MLI beyond obtaining the same quasi-optima as INTERP. According to the efficiency of finding the quasi-optima, the idea of M-Leap might be extended to other training tasks, especially those requiring numerous optimizations, such as training adaptive quantum circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06986 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multilevel leapfrogging initialization for quantum approximate optimization algorithm Ni, Xiao-Hui Cai, Bin-Bin Liu, Hai-Ling Qin, Su-Juan Gao, Fei Wen, Qiao-Yan Quantum Physics Recently, Zhou et al. have proposed a novel Interpolation-based (INTERP) strategy to generate the initial parameters for the Parameterized Quantum Circuit (PQC) in Quantum Approximate Optimization Algorithm (QAOA). INTERP produces the guess of the initial parameters at level $i+1$ by applying linear interpolation to the optimized parameters at level $i$, achieving better performance than random initialization (RI). Nevertheless, INTERP consumes extensive running costs for deep QAOA because it necessitates optimization at each level of the PQC. To address this problem, a Multilevel Leapfrogging Interpolation (MLI) strategy is proposed. MLI can produce the guess of the initial parameters from level $i+1$ to $i+l$ ($l>1$) at level $i$, omitting the optimization rounds from level $i+1$ to $(i+l-1)$. The final result is that MLI executes optimization at few levels rather than each level, and this operation is referred to as Multilevel Leapfrogging optimization (M-Leap). The performance of MLI is investigated on the Maxcut problem. Compared with INTERP, MLI reduces most optimization rounds. Remarkably, the simulation results demonstrate that MLI can achieve the same quasi-optima as INTERP while consuming only 1/2 of the running costs required by INTERP. In addition, for MLI, where there is no RI except for level $1$, the greedy-MLI strategy is presented. The simulation results suggest that greedy-MLI has better stability (i.e., a higher average approximation ratio) than INTERP and MLI beyond obtaining the same quasi-optima as INTERP. According to the efficiency of finding the quasi-optima, the idea of M-Leap might be extended to other training tasks, especially those requiring numerous optimizations, such as training adaptive quantum circuits. |
| title | Multilevel leapfrogging initialization for quantum approximate optimization algorithm |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2306.06986 |