Solving Currency Arbitrage with D-Wave Advantage2 Quantum Annealer Demonstrates Efficient Optimization

Currency arbitrage, the practice of exploiting price differences in currencies across different markets, presents a complex optimisation challenge, and researchers are now turning to quantum computing to find faster solutions. Lorenzo Mazzei, Giada Beccari, and Mirko Laruina, all from the University of Pisa, alongside Marco Cococcioni, demonstrate how quantum annealing can effectively tackle this problem, formulating currency arbitrage as a Quadratic Unconstrained Boolean Optimisation problem suitable for quantum computation. The team tests their approach using the D-Wave Advantage2 computer, representing a significant step towards harnessing the power of quantum computers for real-world financial optimisation, and potentially offering faster, more efficient arbitrage strategies. This work showcases a novel application of quantum annealing, and establishes a benchmark for comparing quantum and classical approaches to a critical financial problem.

Quantum annealing presents a powerful tool for solving complex optimization problems, and companies are increasingly investing in this emerging quantum computing market. This research explores the application of quantum annealing to the Currency Arbitrage (CA) problem, a financial challenge involving identifying profitable currency exchange opportunities, and assesses its performance against established classical methods. The speed and capabilities of the D-Wave quantum annealer are tested, utilising the recently released Advantage 2 prototype.

Currency Arbitrage via Quantum Annealing Formulation

Researchers developed a novel methodology to apply Quantum Annealing to the Currency Arbitrage (CA) problem, a complex financial optimization task. This involved defining binary variables to represent the presence or absence of a specific currency at a given position within a potential arbitrage loop. The team meticulously constructed a QUBO model, utilising a matrix and a vector to minimize a function that captures the profitability of currency exchange loops.

To quantify profitability, scientists computed a profitability factor for each loop, determined by the product of exchange rates along the loop’s sequence of currencies. The methodology requires considering loops with fewer currencies to create a non-trivial optimization challenge. The research leverages the capabilities of the D-Wave Advantage 2 quantum annealer to solve the formulated QUBO problem. Performance comparisons were then conducted between the quantum annealing approach and classical algorithms, evaluating both the ability to identify optimal solutions and the execution time required. The work centers on constructing a QUBO matrix representing the currency exchange rates and constraints, where coefficients correspond to weights and binary variables define the currency loop positions. Specifically, the Hamiltonian incorporates weighted terms, each governing different aspects of the CA problem and constraints. The team meticulously defined how each term contributes to the QUBO matrix, detailing the conditions under which specific coefficients are applied.

For example, one coefficient applies when currency ‘i’ precedes currency ‘j’ in the loop, while another activates when currencies ‘i’ and ‘j’ are distinct at the same position. Other terms depend on currency matches at the loop’s start/end and adjacent positions. Experiments focused on determining the number of computational steps required by each algorithm to first identify the optimal solution. Results demonstrate that Simulated Annealing required the highest number of steps to reach the optimum, while D-WaveSampler achieved faster performance. Notably, TabuSampler consistently identified the optimal solution in just one step, potentially due to its efficient heuristic rules for smaller problem sizes. The team used D-Wave’s ExactSolver to establish a ground truth optimal solution, allowing for accurate comparison of step counts across algorithms. Researchers successfully transformed the task of identifying profitable currency exchange loops into a format suitable for quantum computation, enabling evaluation on the D-Wave Advantage 2 system. The method involves representing potential currency loops with binary variables and minimizing a function that reflects the profitability of each loop, leveraging logarithmic transformations to manage computational complexity. Results indicate that Quantum Annealing offers a competitive approach to solving Currency Arbitrage, demonstrating performance comparable to classical methods in both identifying optimal solutions and execution speed.

The study highlights the potential of quantum techniques for tackling complex financial optimization problems. Authors acknowledge that the performance is influenced by the specific characteristics of the quantum hardware and the problem instance, and further research is needed to explore the scalability and robustness of the approach with larger and more complex datasets. Future work could focus on refining the QUBO formulation and exploring hybrid quantum-classical algorithms to further enhance performance and address limitations inherent in current quantum annealers.