Key points in this article
Quantum hardware has qubit limits, but portfolio universes routinely contain 30–100+ assets. Q72 uses spectral clustering to partition the universe into correlation-coherent sub-groups, runs the quantum stage in parallel across clusters, then recombines. This preserves the correlation structure that makes the portfolio problem meaningful.
One of the most common questions we receive from technically sophisticated users is straightforward: quantum hardware has qubit limits. Portfolio universes routinely contain 30, 50, or 100 assets. How does Q72 apply quantum optimization to portfolios larger than the hardware can represent directly?
The answer involves a pre-processing stage that runs before any quantum circuit executes: spectral clustering. The technique partitions the asset universe into structurally coherent sub-groups, reduces the problem to a tractable size for quantum processing, and does so in a way that preserves the correlation structure that makes the portfolio problem meaningful in the first place.
01Why naive decomposition doesn't work
The obvious approach to a large universe is to divide it arbitrarily — take the first 20 assets, optimize them, take the next 20, optimize those, combine the results. This approach is computationally straightforward and produces reliably bad results. The reason is that portfolio optimization is fundamentally about exploiting the correlation structure between assets. An arbitrary partition destroys this structure.
Quantum hardware has qubit limits, but portfolio universes routinely contain 30–100+ assets.
02Spectral clustering: the intuition
Spectral clustering is a technique from graph theory and machine learning that partitions a set of objects based on their pairwise relationships — in this case, the correlation matrix of asset returns. The clustering algorithm finds the partition of this graph that minimizes the connections between groups relative to the connections within groups.
Intuitively, this produces clusters of assets that are 'close' to each other in correlation space — assets that tend to move together — while ensuring that the connections between clusters are as weak as possible. Each cluster is internally coherent, and the clusters together span the full correlation structure of the universe.

03How this integrates with Q72's quantum stage
In Q72, spectral clustering runs as the first step in the optimization pipeline for any universe above the direct quantum processing threshold. The quantum stage then runs in parallel across all clusters simultaneously, producing an optimized sub-portfolio for each cluster. The final step recombines the cluster results into a single portfolio allocation.
04What this means for portfolio quality
The practical effect is that the quality of the quantum optimization does not degrade significantly as the universe grows. This is not a compromise. Spectral clustering is itself a well-validated technique with a strong theoretical foundation and decades of empirical support in financial applications.




