Differential Evolution VQE for Crypto-currency Arbitrage. Quantum Optimization with many local minima

TL;DR

This paper presents a differential evolution-based VQE optimization method for crypto-currency arbitrage, demonstrating improved convergence over traditional optimizers and feasibility on real quantum hardware, indicating potential quantum advantage.

Contribution

Introduces a novel DE-based VQE optimizer for arbitrage problems, outperforming standard methods and validated on IBM quantum hardware.

Findings

DE optimizer converges to global minimum more effectively than COBYLA

Successful execution on IBM quantum hardware with up to 127 qubits

Potential for quantum advantage in complex financial optimization problems

Abstract

Crypto-currency markets are known to exhibit inefficiencies, which presents opportunities for profitable cyclic transactions or arbitrage, where one currency is traded for another in a way that results in a net gain without incurring any risk. Quantum computing has shown promise in financial applications, particularly in resolving optimization problems like arbitrage. In this paper, we introduce a differential evolution (DE) optimization algorithm for Variational Quantum Eigensolver (VQE) using Qiskit framework. We elucidate the application of crypto-currency arbitrage using different VQE optimizers. Our findings indicate that the proposed DE-based method effectively converges to the optimal solution in scenarios where other commonly used optimizers, such as COBYLA, struggle to find the global minimum. We further test this procedure's feasibility on IBM's real quantum machines up to 127 qubits. With a three-currency scenario, the algorithm converged in 417 steps over a 12-hour period on the "ibm_geneva" machine. These results suggest the potential for achieving a quantum advantage in solving increasingly complex problems.