Portfolio construction using a sampling-based variational quantum scheme

TL;DR

The paper tackles ETF-style portfolio optimization under realistic constraints by adopting a sampling-based CVaR-VQA in a quantum–classical workflow. It introduces a binary reformulation and a problem-reduction strategy to fit current quantum devices, then demonstrates two entanglement maps and two ansätze within a CVaR-VQA framework, optimized with an NFT classical updater and complemented by local-search post-processing. Experiments include 31-qubit simulations and 109-qubit IBM hardware runs, showing that entangled, harder-to-simulate circuits can improve convergence and that the quantum–classical approach can outperform pure classical local search, even under hardware noise. The work highlights a viable path for applying quantum optimization to portfolio workflows and motivates scaling studies toward larger, industry-relevant problem sizes, while acknowledging current hardware limitations and proposing future training and transfer techniques.

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.

Figures (6)

• Figure 1: The workflow of sampling-based VQA. Only step 2. involves a quantum processing unit (QPU).
• Figure 2: a) General design of the ansatz $V(\theta)$. b) Bilinear entanglement. c) The colored entanglement is defined over a 3-label coloring on the IBM's heavy hex chip topology.
• Figure 3: Tuning of $\alpha$ and $r$ for a) the TwoLocal bilinear ansatz and b) the BFCD bilinear ansatz, based on 31-qubit experiments on simulator.
• Figure 4: Comparison of ansatz convergence on hardware and simulator, without local search for the 109-qubit problem. Left: CVaR. Right: best cost found at each iteration (shaded area) and respective moving average (line). Dots mark the NFT epochs.
• Figure 5: Distributions of the objective values sampled from each ansatz at the end of the optimization, benchmarked against the 'Initial' distribution (i.e. iteration 1 on simulator of the the TwoLocal bilinear). Numbers in brackets indicate the iterations performed in the respective run.