Portfolio construction using a sampling-based variational quantum scheme

ArXiv ID: 2508.13557 “View on arXiv”

Authors: Gabriele Agliardi, Dimitris Alevras, Vaibhaw Kumar, Roberto Lo Nardo, Gabriele Compostella, Sumit Kumar, Manuel Proissl, Bimal Mehta

Abstract

The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variational Quantum Algorithm (VQA), combined with a local-search post-processing, for solving problem instances that beyond a certain size become classically hard. We also propose a problem formulation that is suited for sampling-based VQA. Our utility-scale experiments on IBM Heron processors involve 109 qubits and up to 4200 gates, achieving a relative solution error of 0.49%. Results indicate that a combined quantum-classical workflow achieves better accuracy compared to purely classical local search, and that hard-to-simulate quantum circuits may lead to better convergence than simpler circuits. Our work paves the path to further explore portfolio construction with quantum computers.

Keywords: quantum computing, Variational Quantum Algorithm (VQA), portfolio optimization, CVaR, IBM Heron, Equities (ETF)

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces a novel quantum algorithm (CVaR-VQA) and modifies a quadratic optimization problem for quantum sampling, involving advanced quantum mechanics and non-trivial mathematical formulation. It is backed by utility-scale experiments on IBM Heron processors with 109 qubits, concrete error metrics (0.49% relative error), and a direct comparison to classical solvers (CPLEX), making it highly implementation-heavy and data-driven.
  flowchart TD
    A["Research Goal: Solve large-scale portfolio optimization with constraints using quantum-classical hybrid"] --> B["Data: ETF equity dataset; Real-world constraints"]
    B --> C["Method: Sampling-based CVaR VQA with local search post-processing"]
    C --> D{"Computational Process: Run on IBM Heron<br/>109 qubits, 4200 gates"}
    D --> E["Outcomes: 0.49% relative error<br/>Better accuracy than classical local search<br/>Hard-to-simulate circuits improve convergence"]