统计套利投资组合中用于资产聚类的高斯玻色子采样
Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios
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中文总结 AI 辅助
研究将标准普尔500指数残差相关数据映射到GBS兼容邻接矩阵，用GBS Boost和GBS Roots两种量子聚类算法与经典算法对比，在滚动一年窗口构建投资组合，发现量子聚类在高波动时表现优，为量化金融应用奠定量子基础。
中文摘要 AI 辅助
高斯玻色子采样（GBS）为从邻接矩阵中采样密集子图提供了一种原生光子量子启发式方法，为组合图搜索问题提供了一种可扩展的物理方法。同时，相关矩阵聚类算法，如谱聚类和SPONGE，已为在统计套利（StatArb）策略中从相关矩阵识别联动资产建立了强大的基准。在这项工作中，我们将标准普尔500指数的残差相关数据映射到与GBS兼容的邻接矩阵中。我们将这些经典聚类算法与两种量子聚类算法GBS Boost和我们新颖的GBS Roots进行基准测试，以在滚动的一年窗口内构建动态、市场中性的投资组合。不同宏观经济状况下的模拟表明，量子聚类在高波动时期的大型股票领域中产生了卓越的阿尔法，有效隔离了结构性市场特质。至关重要的是，这种经济优势在模拟的低损耗条件下持续存在，并通过应用相干位移来补偿光子损失扩展到高损耗状态。我们的发现强调了GBS衍生的图聚类在构建稳健的StatArb投资组合中的功效，为更广泛的量化金融应用奠定了量子基础。
英文摘要
Gaussian Boson Sampling (GBS) provides a native photonic quantum heuristic for sampling dense subgraphs from adjacency matrices, offering a scalable physical approach to combinatorial graph search problems. Simultaneously, correlation matrix clustering algorithms, such as Spectral and SPONGE, have established robust benchmarks for identifying co-moving assets from correlation matrices in statistical arbitrage (StatArb) strategies. In this work, we map S&P 500 residual correlation data into GBS-compatible adjacency matrices. We benchmark those classical clustering algorithms against two quantum clustering algorithms, GBS Boost and our novel GBS Roots, to construct dynamic, market-neutral portfolios over a rolling one-year window. Simulations across distinct macroeconomic regimes reveal that quantum clustering generates superior alpha within large stock universes during periods of high volatility, effectively isolating structural market idiosyncrasies. Crucially, this economic advantage persists under simulated low-loss conditions and extends into high-loss regimes via the application of coherent displacement to compensate for photon loss. Our findings underscore the efficacy of GBS-derived graph clustering in constructing robust StatArb portfolios, establishing a quantum foundation for broader quantitative finance applications.
