Currency Arbitrage Optimization using Quantum Annealing, QAOA and Constraint Mapping

TL;DR

The paper addresses identifying profitable currency-arbitrage cycles in a directed graph with edge rates $r_{ij}$ by formulating the problem as a QUBO with $C_{tot}=C+m_pP$ and binary variables $b_{ij}$. It then explores three translation paths—NchooseK constraint mapping, IBM Quantum native formats for QAOA, and direct quantum annealing via D-Wave—comparing their performance on both quantum annealers and gate-based hardware. The study reports that D-Wave-based solutions converge rapidly to optimal-like cycles, while QAOA on IBM Qiskit often yields suboptimal or constraint-violating results under current hardware conditions, highlighting embedding and noise challenges. Overall, the work demonstrates the potential of near-term quantum methods for financial optimization while clearly outlining the practical limitations and areas for improvement in formulation, parameter tuning, and hardware deployment.

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.

Figures (5)

• Figure 1: Flowchart of the Algorithm
• Figure 2: Quantum Circuit with Optimal Parameters, with 1 Layer
• Figure 3: 4-Currencies' Frequency of Annealing Shots vs. Profit of Degenerate Energy Solutions in NchooseK Ocean Solver. Notice that the Best Solution is included in the Solution Space.
• Figure 4: 5-Currencies' Frequency of Annealing Shots vs. Profit of Degenerate Energy Solutions in NchooseK Ocean Solver.
• Figure 5: 6 Currencies' Frequency of Annealing Shots vs. Profit of Degenerate Energy Solutions in NchooseK Ocean Solver.