Finding Arbitrage with different Quantum Algorithms

Finding Arbitrage with different Quantum Algorithms

Abstract:

Quantum computing, a discipline that leverages the principles of quantum physics to perform complex calculations, has emerged as a transformative field since its initial conceptualization by Richard Feynman and Yuri Manin in the 1980s. Recent advancements in quantum hardware, coupled with a surge in investment, have accelerated the application of quantum computing across a diverse range of sectors with one of them being finance. Financial operations often boil down to combinatoric optimization problems, which makes them are well suited to quantum methods. Specifically, this work focuses on identifying optimal arbitrage opportunities in financial markets, such as currency exchange. Arbitrage can be framed as a combinatorial optimization problem, solvable through quantum annealing or quantum gate-based computing methods.
Building on the foundation laid by Gili Rosenberg, this work explores the efficacy of quantum annealing and conducts comprehensive benchmarks against other quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA). Also a novel oracle encoding enhanced by Quantum Fourier Transformation (QFT) to solve the arbitrage problem using Grover’s algorithm is introduced. Recognizing that the number of qubits and the size of the quantum circuit are among today’s major computational bottlenecks, recently established pre-processing and post-processing techniques are employed to optimize computational efficiency across the various quantum algorithms studied.

(This research was produced in cooperation with Aqarios GmbH)

Author:

Jakob Anton Mayer

Advisors:

Jonas Nüßlein, Jonas Stein, Nico Kraus, Claudia Linnhoff-Popien

Student Thesis | Published March 2024 | Copyright © QAR-Lab
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