突破散粒噪声极限：用于量子优化的缓存回收方差缩减梯度

中文摘要 AI 辅助

变分量子算法（VQA）严重依赖经典优化程序来导航高维、含噪的参数景观。然而，通过参数平移规则评估解析梯度需要 $\mathcal{O}(p)$ 次电路执行，这使得该方法对于深层电路在计算上变得不可行。虽然同时扰动方法提供了 $\mathcal{O}(1)$ 的替代方案，但其梯度估计遭受严重的 $\mathcal{O}(p)$ 空间方差，这阻碍了收敛。为解决这一矛盾，我们通过利用方差缩减技术引入了缓存回收方差缩减梯度（CRVG）。我们提出了两种变体：3-电路（单侧）非递归CRVG和递归CRVG。通过引入中心点缓存机制，3-电路CRVG在数学上回收量子测量，将两种变体的内循环电路复杂度降低了25%。我们建立了两种路由路径之间的理论分离，以达到 $\epsilon^2$-稳定点：非递归变体达到 $\mathcal{O}(\max\{p/\epsilon^2, p^{2/3}/\epsilon^{10/3}\})$ 的样本复杂度，而递归变体实现了改进的复杂度 $\mathcal{O}(\max\{p/\epsilon^2, \sqrt{p}/\epsilon^3\})$。在实验上，对MaxCut和最大独立集（MIS）基准的广泛评估验证了这些发现。虽然标准同时扰动在不同深度下仍然是一个稳健的基线，但CRVG在特定的可摊销机制中展示了针对性的优势，例如非递归变体在EfficientSU2电路上以及两种变体在深度三的QAOA上，产生了更优的能量最小值和更紧的输出方差。最终，CRVG为扩展近期量子优化建立了一个原则性的偏差-吞吐量权衡。

英文摘要

Variational Quantum Algorithms (VQAs) rely heavily on classical optimization routines to navigate high-dimensional, noisy parameter landscapes. However, the evaluation of analytical gradients via the parameter-shift rule requires $\mathcal{O}(p)$ circuit executions, rendering this approach computationally prohibitive for deep circuits. While simultaneous perturbation methods provide an $\mathcal{O}(1)$ alternative, their gradient estimates suffer from severe $\mathcal{O}(p)$ spatial variance, which impedes convergence. To resolve this tension, we introduce the Cached Recycled Variance-Reduced Gradient (CRVG) by leveraging variance reduction techniques. We formulate two variants: a 3-Circuit (1-Sided) Non-Recursive CRVG and a Recursive CRVG. By introducing a center-point caching mechanism, the 3-Circuit CRVG mathematically recycles quantum measurements to reduce the inner-loop circuit complexity by 25\% across both variants. We establish a theoretical separation between the two routing paths to achieve an $ε^2$-stationary point: the non-recursive variant reaches a sample complexity of $\mathcal{O}(\max\{p/ε^2, p^{2/3}/ε^{10/3}\})$, while the recursive variant achieves an improved complexity of $\mathcal{O}(\max\{p/ε^2, \sqrt{p}/ε^3\})$. Empirically, extensive evaluations on MaxCut and Maximum Independent Set (MIS) benchmarks validate these findings. While standard simultaneous perturbation remains a robust baseline across varying depths, CRVG demonstrates targeted advantages in specific amortizable regimes, such as the non-recursive variant on EfficientSU2 circuits and both variants on depth-three QAOA, yielding superior energy minimums and tighter output variances. Ultimately, CRVG establishes a principled bias-throughput trade-off for scaling near-term quantum optimization.

发表机构

• IBM Research（IBM研究院）

机构由 AI 辅助整理，请以论文原文为准。