Currency Arbitrage Optimization using Quantum Annealing, QAOA and Constraint Mapping

ArXiv ID: 2502.15742 “View on arXiv”

Authors: Unknown

Abstract

Currency arbitrage capitalizes on price discrepancies in currency exchange rates between markets to produce profits with minimal risk. By employing a combinatorial optimization problem, one can ascertain optimal paths within directed graphs, thereby facilitating the efficient identification of profitable trading routes. This research investigates the methodologies of quantum annealing and gate-based quantum computing in relation to the currency arbitrage problem. In this study, we implement the Quantum Approximate Optimization Algorithm (QAOA) utilizing Qiskit version 1.2. In order to optimize the parameters of QAOA, we perform simulations utilizing the AerSimulator and carry out experiments in simulation. Furthermore, we present an NchooseK-based methodology utilizing D-Wave’s Ocean suite. This methodology enables a comparison of the effectiveness of quantum techniques in identifying optimal arbitrage paths. The results of our study enhance the existing literature on the application of quantum computing in financial optimization challenges, emphasizing both the prospective benefits and the present limitations of these developing technologies in real-world scenarios.

Keywords: quantum annealing, QAOA, combinatorial optimization, currency arbitrage, graph algorithms, foreign exchange

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical constructs like QUBO formulations and specific combinatorial optimization constraints (NchooseK) with detailed derivations. However, it lacks real-world data backtesting, relying solely on small synthetic exchange rate tables and simulator runs without performance metrics like Sharpe ratios or latency analysis.

  flowchart TD
    Start["Research Goal<br>Identify optimal arbitrage paths<br>using Quantum Annealing & QAOA"] --> Inputs["Data Inputs<br>Historical FX Rates (e.g., JPY/USD/GBP)"]
    
    Inputs --> Methodology
    subgraph Methodology ["Methodology: Comparative Analysis"]
        direction LR
        QAOA["QAOA Implementation<br>(Qiskit 1.2 + AerSimulator)"] --> Sim["Parameter Optimization & Simulation"]
        Anneal["Annealing Implementation<br>(D-Wave Ocean / NchooseK)"] --> Hybrid["Constraint Mapping"]
    end

    Methodology --> Eval["Computational Process<br>Comparison of Quantum Techniques<br>(Efficiency & Path Identification)"]
    Eval --> Results["Key Findings<br>Proof of concept for quantum finance<br>Benefits & Limitations in real-world scenarios"]