Quantum Graph Clustering for Statistical Arbitrage Portfolios

Summary

The study maps residual correlations among S&P 500 stocks into adjacency matrices for Gaussian Boson Sampling, a photonic quantum method for sampling dense subgraphs. It compares two classical clustering approaches, Spectral and SPONGE, with the quantum methods GBS Boost and the proposed GBS Roots. The resulting clusters are used to form dynamic, market-neutral statistical arbitrage portfolios over rolling one-year windows.

Simulations across macroeconomic regimes report stronger alpha from quantum clustering in large stock universes during periods of high volatility. The reported advantage persists in simulated low-loss conditions and extends to high-loss conditions when coherent displacement is used to compensate for photon loss. These are simulation results, and the document does not provide specific performance estimates, implementation costs, or evidence from live trading. Its claims therefore concern the tested portfolio construction setup rather than established real-world performance.

Key ideas

• The method converts residual stock correlations into graph matrices suitable for Gaussian Boson Sampling.
• GBS Boost and GBS Roots are compared with Spectral and SPONGE clustering methods.
• Clusters are used to construct dynamic, market-neutral statistical arbitrage portfolios.
• Simulations report a quantum-clustering alpha advantage in large universes during high-volatility regimes.
• The reported robustness to photon loss relies in part on simulated coherent displacement.

Tags

# Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios


# Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.