[Paper] A Quantum-Driven Evolutionary Framework for Solving High-Dimensional Sharpe Ratio Portfolio Optimization

Source: arXiv - 2601.11029v1

Overview

The paper presents a Quantum‑Hybrid Differential Evolution (QHDE) algorithm designed to tackle the notoriously hard problem of high‑dimensional portfolio optimization under Sharpe‑ratio maximization. By recasting the constrained financial model as an unconstrained single‑objective problem and injecting quantum‑inspired probabilistic operators into a classic evolutionary framework, the authors achieve dramatically faster convergence and higher solution quality on portfolios ranging from 20 to 80 assets.

Key Contributions

• Unified Sharpe‑ratio model with adaptive penalty terms that embed all investment constraints directly into the objective, eliminating the need for separate feasibility checks.
• Quantum‑inspired population dynamics: a Schrödinger‑style probabilistic update rule is layered onto standard Differential Evolution (DE) to diversify search directions.
• Chaos‑based reverse learning initialization using good‑point sets, producing a well‑spread initial population that speeds up early convergence.
• Dynamic elite pool + Cauchy‑Gaussian hybrid perturbation to maintain global exploration and avoid premature stagnation.
• Extensive benchmarking on CEC test suites and real‑world asset sets (20‑80 securities), showing up to 73.4 % performance gains over seven leading meta‑heuristics.

Methodology

1. Problem Reformulation – The classic Sharpe‑ratio maximization with constraints (budget, cardinality, turnover, etc.) is transformed into a single‑objective function by adding adaptive penalty terms. The penalties grow when constraints are violated, steering the optimizer back into feasible regions while preserving the financial meaning of the objective.

2. Quantum Hybrid Differential Evolution

   • Base DE: standard mutation, crossover, and selection operators that evolve a population of candidate portfolios.
   • Quantum‑inspired step: each candidate’s vector is treated as a quantum state; a probabilistic “wave‑function collapse” (derived from a Schrödinger‑like equation) determines a new position, allowing jumps that are not limited to the linear combinations typical of DE.
   • Chaos reverse learning: a low‑discrepancy good point set is perturbed by a chaotic map, then reversed to seed the initial population, ensuring maximal dispersion across the search space.

3. Exploration Enhancements

   • Dynamic elite pool stores the best solutions found so far; its composition adapts based on recent improvements.
   • Cauchy‑Gaussian hybrid perturbation applies heavy‑tailed Cauchy jumps combined with fine‑grained Gaussian tweaks to the elite pool, balancing long‑range exploration with local refinement.

4. Algorithm Flow – Initialize population → quantum‑chaotic update → DE mutation/crossover → elite‑pool update with hybrid perturbation → selection → repeat until stopping criteria (max generations or convergence).

Results & Findings

• Precision: QHDE consistently finds Sharpe ratios closer to the known global optimum (or best‑known) across all benchmark dimensions.
• Robustness: Standard deviation of results across 30 independent runs drops by ~40 %, indicating less sensitivity to random seed.
• Scalability: Performance gains increase with problem dimensionality, confirming the algorithm’s suitability for large asset universes.

Practical Implications

• Portfolio construction tools can embed QHDE as a plug‑in optimizer, delivering faster “what‑if” analyses for quantitative analysts handling hundreds of securities.
• Risk‑adjusted return engines (e.g., robo‑advisors) benefit from the algorithm’s ability to respect real‑world constraints (minimum holdings, turnover limits) without costly feasibility post‑processing.
• Cloud‑native services: The quantum‑inspired operators are lightweight and parallelizable, making QHDE a good fit for distributed compute environments (e.g., Kubernetes jobs) where many portfolios are evaluated simultaneously.
• Educational platforms: The clear separation between the financial model and the evolutionary engine provides a teaching example for interdisciplinary courses on computational finance and AI.

Limitations & Future Work

• Parameter sensitivity: The adaptive penalty coefficients and the balance between Cauchy and Gaussian perturbations still require empirical tuning for each new asset class.
• Quantum analogy: While “quantum‑inspired,” the method does not leverage actual quantum hardware; future research could explore hybrid quantum‑classical implementations to further accelerate convergence.
• Constraint coverage: The current formulation assumes convex constraints; extending the penalty framework to handle non‑convex regulatory rules (e.g., sector caps with step functions) remains an open challenge.
• Real‑time trading: The algorithm’s batch‑oriented nature may need adaptation (e.g., incremental updates) for ultra‑low‑latency trading systems.

Bottom line: By marrying quantum‑style probabilistic updates with a proven evolutionary backbone, the QHDE framework offers a compelling, high‑performance alternative for developers building next‑generation portfolio optimization engines. Its demonstrated speedups and robustness make it a promising candidate for production‑grade financial analytics pipelines.

Authors

• Mingyang Yu
• Jiaqi Zhang
• Haorui Yang
• Adam Slowik
• Huiling Chen
• Jing Xu

Paper Information

• arXiv ID: 2601.11029v1
• Categories: cs.NE
• Published: January 16, 2026
• PDF: Download PDF