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Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios

This paper demonstrates that Gaussian Boson Sampling-based quantum clustering algorithms outperform classical methods in constructing robust, market-neutral statistical arbitrage portfolios from S&P 500 data, particularly during high-volatility periods and under simulated photon loss conditions.

Original authors: Dayne Marcus Lopena, Daniel Buguks, Zhenghao Li, Ewan Mer, Shana H. Winston, Shang Yu, Mihai Cucuringu, Del Rajan, Philip Intallura, Raj B. Patel

Published 2026-07-22

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CC BY 4.0

Original authors: Dayne Marcus Lopena, Daniel Buguks, Zhenghao Li, Ewan Mer, Shana H. Winston, Shang Yu, Mihai Cucuringu, Del Rajan, Philip Intallura, Raj B. Patel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the stock market as a giant, chaotic dance floor where millions of people are moving to the same beat, but everyone is trying to find their perfect dance partner. In the world of finance, traders are constantly looking for pairs of stocks that move together like best friends. If one friend suddenly runs away from the group, the other usually follows shortly after. Traders bet on this reunion, buying the one that fell and selling the one that rose, hoping to catch the profit when they snap back together. This is called "Statistical Arbitrage," and the key to making money is finding the right groups of friends quickly and accurately.

To do this, scientists use math to map out who is friends with whom, creating a giant web of connections. But as the web gets bigger, finding the best groups becomes a nightmare for regular computers; it's like trying to find a specific needle in a haystack that keeps growing. Enter the world of quantum physics, specifically a fancy trick called "Gaussian Boson Sampling" (GBS). Think of GBS as a magical, light-based machine that doesn't just count things, but actually feels the shape of the web. It uses particles of light (photons) that bounce around in a maze of mirrors and splitters. Because light behaves in weird, quantum ways, this machine can instantly spot the tightest, most connected groups of friends in the web, a task that would take a normal computer forever to figure out. The big question is: can this light-based magic actually make better trading decisions than the old-school math we use today?

This paper is a story about testing that very question. The authors, a team of physicists and finance experts, decided to see if they could use this quantum light machine to organize the S&P 500—the list of the 500 biggest companies in the US—into better trading groups. They didn't just guess; they built a simulation, a virtual playground where they could test their ideas without risking real money. They took the daily price movements of these stocks and turned them into a map, then fed that map into their quantum algorithm. They created two new ways for the machine to work: one called "GBS Boost" and a new, clever method they invented called "GBS Roots." They then pitted these quantum methods against the best traditional computer algorithms used by finance experts today.

The results were exciting, but with a few important caveats. In their simulations, the quantum methods, especially "GBS Roots," found trading groups that made more money than the traditional methods, particularly when the market was wild and scary. It seems the quantum machine is really good at spotting the hidden, structural quirks in the market that other methods miss, especially during times of high stress like the 2008 crash or the 2020 pandemic crash. However, the paper also found that this magic isn't perfect. If the light particles get lost or scattered (a problem called "photon loss"), the quantum machine starts to stumble and performs worse than the old-school computers. But here is the cool part: the team found a way to fix this by adding a little "push" of light, called "coherent displacement," which acts like a stabilizer. With this fix, the quantum methods stayed strong and competitive even when things got messy.

The authors are careful to say that this is all happening in a simulation right now, not on a real trading floor with real money. They also point out that simply finding the "densest" group of friends isn't always the best way to make money; sometimes, the best groups are a bit more diverse. They suggest that while the quantum approach is a powerful new tool, it works best when the market is volatile and the light particles aren't getting lost. So, while we aren't buying stocks with light beams just yet, this paper suggests that in the future, when our quantum computers are powerful enough, they might just be the secret weapon traders need to navigate the wildest market dances.

Technical Summary: Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios

Problem Statement
The paper addresses the challenge of constructing robust Statistical Arbitrage (StatArb) portfolios by identifying optimal clusters of co-moving assets. Traditional StatArb strategies rely on mean reversion, assuming that price deviations among highly correlated assets are temporary. The core difficulty lies in accurately partitioning large financial correlation graphs into clusters that maximize intra-cluster correlations while minimizing inter-cluster correlations. While classical clustering algorithms (e.g., Spectral, SPONGE) exist, the authors investigate whether photonic quantum computing, specifically Gaussian Boson Sampling (GBS), can offer a superior heuristic for this combinatorial graph search problem. The study specifically targets the "Max-Agree Correlation Clustering Problem" (MACCP), aiming to find a graph partition that maximizes the sum of intra-cluster edge weights (correlations).

Methodology
The authors propose a framework that maps S&P 500 residual correlation data into GBS-compatible adjacency matrices. The workflow involves:

Data Processing: Constructing a residual-return correlation matrix from stock price data, zeroing the main diagonal to create an adjacency matrix for a weighted graph where nodes represent stocks and edges represent pairwise correlations.
Quantum Clustering Algorithms:
- GBS Boost: An adapted algorithm that uses GBS to sample dense subgraphs, which are then evaluated to select clusters.
- GBS Roots (Novel): A new agglomerative-style clustering algorithm. It iteratively samples subgraphs using a GBS device, calculates their Weighted Density (WD), and greedily constructs a disjoint union of samples to form a cluster. This cluster is removed from the graph, and the process repeats until the graph is fully partitioned. Unlike classical methods, GBS Roots does not require a pre-defined number of clusters ( $K$ ).
Portfolio Construction: Within the resulting clusters, stocks are classified as "winners" or "losers" relative to the cluster mean. A zero-cost, equally weighted contrarian strategy is executed (shorting winners, buying losers) over rolling time windows.
Benchmarking: The quantum methods are compared against classical Spectral and SPONGE clustering algorithms, as well as a quantum-inspired classical algorithm (QIC-GBS).
Simulation Conditions: Simulations were conducted across different stock universe sizes (50 and 100 stocks) and under varying conditions of photon loss ( $l_r$ ). Crucially, the study introduces coherent displacement to compensate for photon loss, stabilizing mean photon numbers to prevent the distribution from collapsing into a thermal random state.

Key Contributions

Novel Algorithm: Introduction of GBS Roots, a greedy, agglomerative clustering method that leverages GBS sampling to partition graphs without requiring a predefined cluster count.
Loss Mitigation Strategy: Demonstration that applying coherent displacement in the presence of photon loss recovers the economic performance of GBS methods, allowing them to remain competitive with classical algorithms even at high loss rates (up to 90% in some contexts), whereas uncompensated loss leads to performance degradation.
Empirical Validation: Provision of empirical evidence that GBS-derived clustering can generate superior alpha in large stock universes during periods of high market volatility, effectively isolating structural market idiosyncrasies.

Results

Performance in Volatile Markets: In a lossless 100-stock universe, quantum algorithms (GBS Roots and GBS Boost) achieved higher cumulative total returns and Sharpe ratios compared to classical benchmarks (Spectral and SPONGE), particularly during high-volatility periods (e.g., 2020).
Stability: Quantum methods exhibited lower standard deviations in returns compared to classical counterparts, suggesting more stable risk-adjusted performance in large universes.
Impact of Loss and Displacement:
- Without displacement, GBS methods underperformed classical algorithms when photon loss exceeded 70%.
- With displacement, GBS methods maintained robust returns and outperformed random clustering baselines across all loss rates.
- The study found that maximizing graph-theoretic metrics like Weighted Density (WD) does not strictly correlate with economic returns; SPONGE achieved the highest WD but trailed quantum methods in total return, indicating that strictly maximizing intra-cluster correlations is insufficient for optimal StatArb performance.
Market Regime Sensitivity: Quantum methods showed strong adaptability and superior risk-adjusted returns during high-volatility regimes (2008, 2020) but showed diminished edges during low-volatility or extended unidirectional trends (2017, 2022).

Significance and Claims
The paper claims to establish a "quantum foundation" for quantitative finance applications by demonstrating the efficacy of GBS-derived graph clustering in constructing StatArb portfolios. The authors emphasize that their findings highlight an empirical quantum advantage rather than a formal complexity-theoretic proof. They argue that while GBS is not expected to solve the NP-hard correlation clustering problem in deterministic polynomial time, it serves as an effective heuristic that generates high-quality approximate solutions.

The work underscores that the economic advantage of GBS persists under simulated low-loss conditions and can be extended to high-loss regimes through coherent displacement. The authors conclude that GBS offers a distinct, mathematically different heuristic for identifying economic market structures, particularly valuable for large, volatile market subsets. They note that current hardware constraints limit definitive quantum advantage demonstrations, but the approach provides a promising pathway for future hybrid quantum-classical optimization in finance.

Technical Summary: Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios

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