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<p>The quantum approximate optimization algorithm (QAOA) represents a promising approach for tackling combinatorial optimization challenges on near-term quantum devices. Central to QAOA optimization is the minimization of the expectation of the problem Hamiltonian for parameterized trial quantum states, which motivates the exploration of advanced optimization techniques. In this study, we propose a novel combinatorial optimization strategy, CNN-CVaR-QAOA, which integrates a convolutional neural network (CNN) with conditional value at risk (CVaR) to optimize QAOA circuits. By replacing the traditional loss function with CVaR and leveraging CNN for variational quantum parameter optimization, we demonstrate the superior efficacy of CNN-CVaR-QAOA through experimental validation on Erdos–Renyi random graphs. Our results show better solutions across various graph configurations. Furthermore, we investigate the influence of the CVaR parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4655_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) on algorithm performance, revealing that lower <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4655_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> values lead to smoother objective functions and improved approximation ratios. This work indicates that CNN-CVaR-QAOA offers significant advantages in optimizing QAOA parameters, particularly in the context of near-term intermediate-scale quantum era, highlighting its potential to enhance QAOA optimization efforts across diverse optimization domains.</p>

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Enhancing quantum approximate optimization with CNN-CVaR integration

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Pengnian Cai,
  • Kang Shen,
  • Tao Yang,
  • Yuanming Hu,
  • Bin Lv,
  • Liuhuan Fan,
  • Zeyu Liu,
  • Qi Hu,
  • Shixian Chen,
  • Yunlai Zhu,
  • Zuheng Wu,
  • Yuehua Dai,
  • Fei Yang,
  • Jun Wang,
  • Zuyu Xu

摘要

The quantum approximate optimization algorithm (QAOA) represents a promising approach for tackling combinatorial optimization challenges on near-term quantum devices. Central to QAOA optimization is the minimization of the expectation of the problem Hamiltonian for parameterized trial quantum states, which motivates the exploration of advanced optimization techniques. In this study, we propose a novel combinatorial optimization strategy, CNN-CVaR-QAOA, which integrates a convolutional neural network (CNN) with conditional value at risk (CVaR) to optimize QAOA circuits. By replacing the traditional loss function with CVaR and leveraging CNN for variational quantum parameter optimization, we demonstrate the superior efficacy of CNN-CVaR-QAOA through experimental validation on Erdos–Renyi random graphs. Our results show better solutions across various graph configurations. Furthermore, we investigate the influence of the CVaR parameter ( \(\alpha \) α ) on algorithm performance, revealing that lower \(\alpha \) α values lead to smoother objective functions and improved approximation ratios. This work indicates that CNN-CVaR-QAOA offers significant advantages in optimizing QAOA parameters, particularly in the context of near-term intermediate-scale quantum era, highlighting its potential to enhance QAOA optimization efforts across diverse optimization domains.