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<p>Classical mean-variance optimization is powerful in theory but fragile in practice, often producing highly concentrated, high-turnover portfolios. Naive equal-weight (1/N) portfolios are more robust but largely ignore cross-sectional information. We propose a quantum stochastic walk (QSW) framework that embeds assets in a weighted graph and derives portfolio weights from the stationary distribution of a hybrid quantum-classical walk. The resulting allocations behave as a “smart 1/N” portfolio: structurally close to equal-weight, but with small, data-driven tilts and a controllable level of trading. On recent S&amp;P 500 universes, QSW portfolios match the diversification and stability of 1/N while delivering higher risk-adjusted returns than both mean-variance and naive benchmarks. A comprehensive hyper-parameter grid search shows that this behavior is structural rather than the result of fine-tuning and yields simple design rules for practitioners. A 34-year, multi-universe robustness study with rolling re-optimization further demonstrates that the QSW optimizer preserves these advantages across market regimes. Overall, the QSW framework improves risk-adjusted performance while maintaining strong diversification and moderate turnover.</p>

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Quantum stochastic walks for portfolio optimization: theory and implementation on financial networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月2日

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  • Yen Jui Chang,
  • Wei-Ting Wang,
  • Yun-Yuan Wang,
  • Chen-Yu Liu,
  • Kuan-Cheng Chen,
  • Ching-Ray Chang

摘要

Classical mean-variance optimization is powerful in theory but fragile in practice, often producing highly concentrated, high-turnover portfolios. Naive equal-weight (1/N) portfolios are more robust but largely ignore cross-sectional information. We propose a quantum stochastic walk (QSW) framework that embeds assets in a weighted graph and derives portfolio weights from the stationary distribution of a hybrid quantum-classical walk. The resulting allocations behave as a “smart 1/N” portfolio: structurally close to equal-weight, but with small, data-driven tilts and a controllable level of trading. On recent S&P 500 universes, QSW portfolios match the diversification and stability of 1/N while delivering higher risk-adjusted returns than both mean-variance and naive benchmarks. A comprehensive hyper-parameter grid search shows that this behavior is structural rather than the result of fine-tuning and yields simple design rules for practitioners. A 34-year, multi-universe robustness study with rolling re-optimization further demonstrates that the QSW optimizer preserves these advantages across market regimes. Overall, the QSW framework improves risk-adjusted performance while maintaining strong diversification and moderate turnover.