顺序哈密顿量组装：增强量子计算机上组合优化问题的训练
Sequential Hamiltonian Assembly: Enhancing the training of combinatorial optimization problems on quantum computers
AI总结：
针对量子机器学习中全局损失函数导致的梯度消失问题，本文提出顺序哈密顿量组装（SHA），通过从局部分量迭代近似损失，并在 Max-Cut 上验证其准确率显著优于传统训练和 Layer-VQE。
摘要：
量子机器学习的一个核心挑战是参数化量子电路（PQC）的设计与训练。与深度学习非常相似，梯度消失对 PQC 的可训练性构成重大障碍，其来源多种多样。其中一个来源是非局部损失函数的存在，这类损失函数需要测量所涉及的大量量子比特子集。为了解决这一问题，并促进使用全局损失函数的量子应用中的参数训练，我们提出了顺序哈密顿量组装（SHA）。SHA 通过从局部分量组装损失来迭代地近似损失。为了进一步证明我们方法的可行性，我们扩展了之前的案例研究，引入了一种新的划分策略、QAOA 与 SHA 之间的新融合方式，并在 Max-Cut 优化问题上对 SHA 进行了评估。仿真结果表明，在 Max-Cut 的平均准确率上，SHA 比传统参数训练高出 43.89%，比经验上的最先进方法 Layer-VQE 高出 29.08%。这为局部性感知学习技术铺平了道路，可缓解一大类实际相关问题中的梯度消失问题。
英文摘要：
A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs). Much like in deep learning, vanishing gradients pose significant obstacles to the trainability of PQCs, arising from various sources. One such source is the presence of non-local loss functions, which require the measurement of a large subset of qubits involved. To address this issue and facilitate parameter training for quantum applications using global loss functions, we propose Sequential Hamiltonian Assembly (SHA). SHA iteratively approximates the loss by assembling it from local components. To further demonstrate the feasibility of our approach, we extend our previous case study by introducing a new partitioning strategy, a new merger between QAOA and SHA, and an evaluation of SHA onto the Max-Cut optimization problem. Simulation results show that SHA outperforms conventional parameter training by 43.89% and the empirical state-of-the-art, Layer-VQE by 29.08% in the mean accuracy for Max-Cut. This paves the way for locality-aware learning techniques, mitigating vanishing gradients for a large class of practically relevant problems.
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