Paper: arXiv 2509.16955

Authors: Chi-Sheng Chen, Aidan Hung-Wen Tsai

Abstract

We formulate automated market maker (AMM) \emph{“rebalancing”} as a binary detection problem and study a hybrid quantum–classical self-attention block, \textbf{“Quantum Adaptive Self-Attention (QASA)”}. QASA constructs quantum queries/keys/values via variational quantum circuits (VQCs) and applies standard softmax attention over Pauli-$Z$ expectation vectors, yielding a drop-in attention module for financial time-series decision making. Using daily data for \textbf{“BTCUSDC”} over \textbf{“Jan-2024–Jan-2025”} with a 70/15/15 time-series split, we compare QASA against classical ensembles, a transformer, and pure quantum baselines under Return, Sharpe, and Max Drawdown. The \textbf{“QASA-Sequence”} variant attains the \emph{“best single-model risk-adjusted performance”} (\textbf{“13.99%”} return; \textbf{“Sharpe 1.76”}), while hybrid models average \textbf{“11.2%”} return (vs.\ 9.8% classical; 4.4% pure quantum), indicating a favorable performance–stability–cost trade-off.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical formalisms including variational quantum circuits, Pauli-Z expectation measurements, and extensive feature engineering with specific encodings, indicating high mathematical density. It also demonstrates high empirical rigor with a defined backtest on real BTC/USDC data (Jan 2024–Jan 2025), a time-series split, and quantitative performance metrics (return, Sharpe, drawdown).

Research Flowchart

  flowchart TD
  A["Research Goal<br>Formulate AMM Rebalancing as Binary Detection<br>Study Quantum Adaptive Self-Attention QASA"] --> B["Data & Baselines"]
  B --> C["Key Methodology: QASA Module"]
  C --> D["Computational Process<br>Hybrid Quantum-Classical Execution"]
  D --> E["Key Findings & Outcomes"]

  subgraph B ["Data & Inputs"]
      B1["Asset: BTCUSDC<br>Period: Jan 2024 - Jan 2025"]
      B2["Split: 70/15/15 Time-Series"]
      B3["Baselines: Classical Ensembles, Transformer, Pure Quantum"]
  end

  subgraph C ["QASA Methodology"]
      C1["VQC Construction<br>Quantum Queries/Keys/Values"]
      C2["Pauli-Z Expectation Vectors"]
      C3["Softmax Attention Mechanism"]
  end

  subgraph D ["Computation"]
      D1["Training: Variational Optimization"]
      D2["Inference: Attention Scoring & Prediction"]
  end

  subgraph E ["Outcomes"]
      E1["Best Single Model: QASA-Sequence<br>Return: 13.99%, Sharpe: 1.76"]
      E2["Hybrid Avg Return: 11.2%<br>vs Classical: 9.8%, Pure Quantum: 4.4%"]
      E3["Trade-off: Favorable Performance-Stability-Cost"]
  end

Cited References (67)

  1. Quantum adaptive self-attention for quantum transformer models (2025) — link
  2. Quantum-enhanced channel mixing in rwkv models for time series forecasting (2025) — link
  3. Quantum long short-term memory (2022)
  4. Linear-layer-enhanced quantum long short-term memory for carbon price forecasting (2023)
  5. Learning to program variational quantum circuits with fast weights (2024)
  6. Long short-term memory (1997)
  7. Attention is all you need (2017)
  8. A multi-source dataset of urban life in the city of Milan and the Province of Trentino (2015)
and 59 more
  1. Long Short-Term Memory (1997) — link
  2. Quantum Machine Learning (2017) — link
  3. RWKV: Reinventing RNNs for the Transformer Era (2023)
  4. Informer: Beyond efficient transformer for long sequence time-series forecasting (2021)
  5. Quantum long short-term memory (QLSTM) vs. classical LSTM in time series forecasting: a comparative study in solar power forecasting (2024)
  6. Differential privacy (2006)
  7. Quantum circuit learning (2018)
  8. R 'e nyi differential privacy (2017)
  9. Quantum machine learning for quantum anomaly detection (2018)
  10. Dynamic differential-privacy preserving sgd (2021) — link
  11. Learning differentially private recurrent language models (2017) — link
  12. Differentially private federated tensor completion for cloud–edge collaborative AIoT data prediction (2023)
  13. Quantum machine learning with differential privacy (2023)
  14. Differential privacy in quantum computation (2017)
  15. Quantum Reinforcement Learning Trading Agent for Sector Rotation in the Taiwan Stock Market — → 2506.20930
  16. Diffusion Models Beat GAN s on Image Synthesis (2021) — link
  17. Classifier-Free Diffusion Guidance (2022) — link
  18. Denoising Diffusion Implicit Models (2020) — link
  19. High-Dimensional Continuous Control Using Generalized Advantage Estimation (2015) — link
  20. Proximal Policy Optimization Algorithms (2017) — link
  21. Variational Quantum Circuits for Deep Reinforcement Learning (2020) — link
  22. Parametrized Quantum Policies for Reinforcement Learning (2021) — link
  23. Quantum Agents in the Gym: A Variational Quantum Algorithm for Deep Q-Learning (2022) — link
  24. Quantum Reinforcement Learning in Continuous Action Space (2025) — link
  25. Quantum Architecture Search via Deep Reinforcement Learning (2021) — link
  26. Quantum Reinforcement Learning Trading Agent for Sector Rotation in the Taiwan Stock Market — → 2506.20930
  27. Quantum Generative Models for Image Generation: Insights from MNIST and MedMNIST (2025) — link
  28. Quantum-Enhanced Natural Language Generation: A Multi-Model Framework with Hybrid Quantum-Classical Architectures (2025) — link
  29. Quantum deep recurrent reinforcement learning (2023)
  30. Denoising Diffusion Probabilistic Models (2020) — link
  31. Score-Based Generative Modeling through Stochastic Differential Equations (2020) — link
  32. Elucidating the Design Space of Classifier-Guided Diffusion Generation (2024) — link
  33. No Training, No Problem: Rethinking Classifier-Free Guidance for Diffusion Models (2024) — link
  34. Uniswap v2 Core (2020) — link
  35. Uniswap v3 Core (2021) — link
  36. Improved Price Oracles: Constant Function Market Makers (2020) — link
  37. Replicating Market Makers (2023) — link
  38. Quantifying Loss in Automated Market Makers (2022) — link
  39. Strategic Liquidity Provision in Uniswap v3 (2021) — link
  40. Risks and Returns of Uniswap V3 Liquidity Providers (2022) — link
  41. DeepLOB: Deep Convolutional Neural Networks for Limit Order Books (2019) — link
  42. TransLOB: Transformer-based Limit Order Book Modeling (2020) — link
  43. Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting (2021) — link
  44. Forecasting realized volatility in turbulent times using temporal fusion transformers (2023) — link
  45. Quantum Machine Learning (2017) — link
  46. Quantum Machine Learning in Feature Hilbert Spaces (2019) — link
  47. Supervised Quantum Machine Learning Models Are Kernel Methods (2021) — link
  48. Option Pricing Using Quantum Amplitude Estimation (2020) — link
  49. Quantum Vision Transformers (2024) — link
  50. Quantum Self-Attention Neural Networks for Text Classification (2022) — link
  51. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle (1989) — link
  52. Analysis of Financial Time Series, 3rd ed. (2010)
  53. Attention Is All You Need (2017) — link
  54. DeepLOB: Deep Convolutional Neural Networks for Limit Order Books (2019) — link
  55. Supervised Learning with Quantum-Enhanced Feature Spaces (2019) — link
  56. Quantum Computing in the NISQ Era and Beyond (2018) — link
  57. Quantum self-attention neural networks for text classification (2024) — link
  58. Benchmarking Classical and Quantum Models for DeFi Yield Prediction on Curve Finance — → 2508.02685
  59. Quantum-Enhanced Natural Language Generation: A Multi-Model Framework with Hybrid Quantum-Classical Architectures (2025) — link

3 of 67 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.