Differential evolution VQE for crypto-currency arbitrage. Quantum optimization with many local minima.

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 scenario of three currencies, the algorithm converged in 417 steps over a 12 hour period on the "ibm_geneva" machine. These results suggest the potential to achieve a quantum advantage in solving increasingly complex problems. • We introduce a differential evolution (DE) optimization algorithm for Variational Quantum Eigensolver (VQE) using Qiskit. • We validate this method using crypto-currency arbitrage, as an example of problem with many local minima. • We test this procedure's feasibility on IBM's real quantum machines up to 127 qubits. [ABSTRACT FROM AUTHOR]