Paper: arXiv 2407.19857

Abstract

Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) infrastructure. Utilizing QC’s applicable strengths to the finance industry’s problems, such as PO, allows us to solve these problems using quantum-based algorithms such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). While the Quantum potential for finance is highly impactful, the architecture and composition of the quantum circuits have not yet been properly defined as robust financial frameworks/algorithms as state of the art in present literature for research and design development purposes. In this work, we propose a novel scalable framework, denoted PO-QA, to systematically investigate the variation of quantum parameters (such as rotation blocks, repetitions, and entanglement types) to observe their subtle effect on the overall performance. In our paper, the performance is measured and dictated by convergence to similar ground-state energy values for resultant optimal solutions by each algorithm variation set for QAOA and VQE to the exact eigensolver (classical solution). Our results provide effective insights into comprehending PO from the lens of Quantum Machine Learning in terms of convergence to the classical solution, which is used as a benchmark. This study paves the way for identifying efficient configurations of quantum circuits for solving PO and unveiling their inherent inter-relationships.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced quantum algorithmic concepts (VQE, QAOA) and intricate circuit parameter tuning, indicating high mathematical complexity. It also demonstrates empirical rigor through systematic experiments comparing quantum algorithms to a classical benchmark across varying risk factors, though it lacks backtest-ready data or real-market implementation details.

Research Flowchart

  flowchart TD
  Start["<b>Research Goal:</b><br>Develop scalable framework PO-QA to analyze<br>quantum parameter variation in PO"] --> Input["<b>Input Data:</b><br>Portfolio Datasets<br>Classical Eigensolver Benchmark"]
  
  Input --> Method["<b>Methodology:</b><br>Iterative Framework PO-QA<br>Testing QAOA & VQE circuits"]
  
  Method --> Process["<b>Computation:</b><br>Parametric Quantum Circuit Execution<br>Rotation Blocks, Repetitions, Entanglement Types"]
  
  Process --> Eval["<b>Evaluation:</b><br>Measure convergence to<br>Classical Ground State Energy"]
  
  Eval --> Results["<b>Key Findings:</b><br>1. Identified optimal QAOA/VQE configurations<br>2. Established parameter-performance relationships<br>3. Created benchmark framework for PO"]
  
  Results --> End["<b>Outcome:</b><br>PO-QA Framework validated<br>Foundation for quantum PO research"]

Cited References (30)

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  2. Portfolio Optimization: A Comparative Study (2023) — link
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  7. Quantum Machine Learning in Finance: Time Series Forecasting (2022) — link
  8. Studying the Impact of Quantum-Specific Hyperparameters on Hybrid Quantum-Classical Neural Networks (2024) — link
and 22 more
  1. Portfolio Selection (1952) — link
  2. The Efficient Frontier in Modern Portfolio Theory (2013)
  3. The Efficient Frontier in Modern Portfolio Theory (2013)
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  5. Quantitative Investment Analysis (2015)
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  7. Quantum optimization using variational algorithms on near-term quantum devices (2018)
  8. Improving Variational Quantum Optimization using CVaR (2020)
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  16. WikipediaDataProvider - Qiskit Finance 0.4.0
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  19. Application of deep quantum neural networks to finance (2022) — link
  20. Financial fraud detection using quantum graph neural networks (2024) — link
  21. QFNN-FFD: Quantum Federated Neural Network for Financial Fraud Detection (2024) — link
  22. The Potential of Quantum Techniques for Stock Price Prediction (2023) — link

0 of 30 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.