Large-scale portfolio optimization using Pauli Correlation Encoding

TL;DR

This paper demonstrates a scalable quantum algorithm for large portfolio optimization by encoding multiple variables per qubit, enabling practical application to real-world financial problems with over 250 variables.

Contribution

It introduces a novel Pauli correlation encoding method for gate-based quantum algorithms, allowing multiple variables per qubit and improving scalability in portfolio optimization.

Findings

Successfully applied to a problem with over 250 variables

Partitioned market graph into sub-portfolios of correlated assets

Enhanced scalability over traditional variational methods

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.