Large-scale portfolio optimization using Pauli Correlation Encoding

TL;DR

This paper addresses scaling gate-based quantum portfolio optimization to more than $m>250$ assets by encoding multiple problem variables per qubit using Pauli Correlation Encoding (PCE) and solving via a variational approach with a Hardware-Efficient Ansatz. A recursive market-graph bipartitioning framework partitions assets into $n_{\text{splits}}+1$ clusters and selects a top-performing representative per cluster. Compared to QAOA and EDAs, PCE demonstrates superior scalability (gate counts $<750$ for large instances) and improved risk-adjusted performance on the Sharpe ratio, with approximately one-hour runtimes on statevector simulation for $m=250$. These results indicate a viable path for quantum-accelerated portfolio optimization on realistic market graphs and motivate future work on circuit architectures and noise resilience.

Abstract

Portfolio optimization is a cornerstone of financial decision-making, traditionally relying on classical algorithms to balance risk and return. Recent advances in quantum computing offer a promising alternative, leveraging quantum algorithms to efficiently explore complex solution spaces and potentially outperform classical methods in high-dimensional settings. However, conventional quantum approaches typically assume a one-to-one correspondence between qubits and variables (e.g. financial assets), which severely limits the applicability of gate-based quantum systems due to current hardware constraints. As a result, only quantum annealing-like methods have been used in realistic scenarios. In this work, we show how a gate-based variational quantum algorithm can be applied to a real-world portfolio optimization problem by assigning multiple variables per qubit. Specifically, we address a problem involving over 250 variables, where the market graph representing a real stock market is iteratively partitioned into sub-portfolios of highly correlated assets. This approach enables improved scalability compared to traditional variational methods and opens new possibilities for quantum-enhanced financial applications.

Figures (9)

• Figure 1: Number of qubits, and layers as a function of the number of variables in the problem to be solved
• Figure 2: HEA built with a linear entangling structure and CZ gates, sued in PCE strategy approach where $m = 10$, $n=4$, $k=2$ and $p=2$.
• Figure 3: Market graph with $m$ nodes where nodes represent stock assets.
• Figure 4: Iterative partition of the market graph (a) with $m=5$ nodes, into two (b) and three (c) subgraphs by performing cuts over the representation. Cuts are represented with red dashed lines, and same color nodes represent correlated assets within the same cluster.
• Figure 5: Aggregate of stock values in S&P 500 stock market along time. Blue and red parts represent training and testing fractions of the dataframe, respectively.