Paper: arXiv 2502.15742

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]