Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios

2026-07-21

AI Summary

This study addresses the challenge of identifying co-moving assets and constructing robust statistical arbitrage portfolios in highly volatile markets by proposing a quantum graph clustering approach based on Gaussian Boson Sampling (GBS). The method maps residual correlations of S&P 500 assets into an adjacency matrix amenable to GBS processing and employs a rolling-window framework to dynamically construct market-neutral portfolios. Key innovations include the introduction of a novel GBS Roots algorithm and the first integration of coherent displacement techniques to mitigate photon loss, substantially enhancing clustering performance under high-loss conditions. Empirical results demonstrate that the proposed approach significantly boosts excess returns during periods of elevated market volatility and maintains consistent outperformance across a wide range of photon loss levels.

Abstract

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.

Problem

• Statistical Arbitrage
• Asset Clustering
• Correlation Matrix
• Market-Neutral Portfolio
• High Volatility

Innovation

• Gaussian Boson Sampling
• quantum clustering
• statistical arbitrage
• coherent displacement
• asset correlation