Variational Quantum Circuit-Based Reinforcement Learning for Dynamic Portfolio Optimization

Paper: arXiv 2601.18811

Authors: Vincent Gurgul, Ying Chen, Stefan Lessmann

Abstract

This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical neural-network-based Deep Deterministic Policy Gradient and Deep Q-Network algorithms. Through an empirical evaluation on real-world financial data, we show that our quantum agents achieve risk-adjusted performance comparable to, and in some cases exceeding, that of classical Deep RL models with several orders of magnitude more parameters. However, while quantum circuit execution is inherently fast at the hardware level, practical deployment on cloud-based quantum systems introduces substantial latency, making end-to-end runtime currently dominated by infrastructural overhead and limiting practical applicability. Taken together, our results suggest that QRL is theoretically competitive with state-of-the-art classical reinforcement learning and may become practically advantageous as deployment overheads diminish. This positions QRL as a promising paradigm for dynamic decision-making in complex, high-dimensional, and non-stationary environments such as financial markets. The complete codebase is released as open source at: https://github.com/VincentGurgul/qrl-dpo-public

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical and mathematical bridge between Variational Quantum Circuits and dynamic reinforcement learning (DDPG/DQN) for portfolio management. The empirical validation uses real-world financial data, offers critical insights into current quantum hardware deployment latencies, and is fully reproducible via a public GitHub repository.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate QRL for Dynamic Portfolio Optimization] --> B[Input Data: Real-World Financial Equities Market Data]
    B --> C[Methodology: Design VQC-based Quantum Analogues of DDPG & DQN]
    C --> D[Execution & Empirical Evaluation: QRL Agents vs Classical Deep RL Models]
    D --> E[Key Finding 1: Quantum agents match/exceed Classical RL with significantly fewer parameters]
    D --> F[Key Finding 2: Cloud quantum hardware latency introduces deployment bottlenecks]

Cited References (129)

1. Quantum Neural Networks : Concepts , Applications , and Challenges (2021) — link
2. Reinforcement learning application in portfolio optimization: a comprehensive literature review (2024) — link
3. Transformation of quantum states using uniformly controlled rotations (2004) — link
4. Recent Developments and Applications in Quantum Neural Network : A Review (2019) — link
5. The quest for a Quantum Neural Network (2014) — link
6. A review of Quantum Neural Networks : Methods , Models , Dilemma (2021) — link
7. ℤ2 × ℤ2 Equivariant Quantum Neural Networks : Benchmarking against Classical Neural Networks (2024) — link
8. Benchmarking adversarially robust quantum machine learning at scale (2023) — link

3 of 129 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.